On the Brink of Nuclear War: Projectile Motion and the Cuban Missile Crisis Instructional Goal: John Clark, Physics Teacher and Military Historian, Deltona HS, Deltona 2012 Naval Historical Foundation STEM-H Teacher Fellowship Skip the sports analogies and offer an integrated, standards based lesson combining Cold War history and the physics of projectile motion to land a missile on target in defense of our nation. With the included activities your students will learn about projectile motion and the importance of precision and accuracy, and the details of the October 1962 Cuban Missile Crisis. Students will learn that, with projectile motion, the movement along the x and y access are independent of each other with primarily the force of gravity acting on the projectile once launched, then work problems related to determining the range of a missile given certain parameters. They will also learn that good problem solving can prevent the launch of projectiles. Common Core State Standards (For Activity 2): CCSS.ELA-Literacy.RH.6-8.2 Determine the central ideas or information of a primary or secondary source; provide an accurate summary of the source distinct from prior knowledge or opinions CCSS.ELA-Literacy.RH.9-10.2 Determine the central ideas or information of a primary or secondary source; provide an accurate summary of how key events or ideas develop over the course of the text. CCSS.ELA-Literacy.RH.11-12.1 Cite specific textual evidence to support analysis of primary and secondary sources, connecting insights gained from specific details to an understanding of the text as a whole.
Next Generation Science Standards (For Activity 1): HS-PS2.A: Forces and Motion, Newton s second law accurately predicts changes in the motion of macroscopic objects. (HS-PS2-1) HS-PS2-2 and H-PS2-4 Use mathematical representations of phenomena to describe explanations. Background: The Cuban Missile Crisis, October 1962. Often referred to as the height of the Cold War the Cuban missile crisis came about in October 1962 when the Soviet Union was discovered installing missile launch sites in the country of Cuba, just 90 miles from the United States. From that proximity a Soviet nuclear missile could quickly reach and destroy a city anywhere along the eastern seaboard causing extensive loss of life and property a vulnerability to attack that the U.S. Government could not tolerate. As we saw with the events of 9/11, an attack on the United States would bring public cries for immediate retaliation and World War III could begin. It was a war both sides knew they could not really win as each had enough nuclear warheads to wipe out every major city in the others country. Life as Americans and Soviets currently lived would cease to exist, with each side dealing with loss of life in the millions and the complete destruction of the infrastructure of each country. Both sides also knew that the pride of each country might cause them to face total destruction rather than capitulate to the actions of the other side. An American spy plane (called the U-2) on patrol over Cuba collected intelligence photos of the launch site construction. The information quickly made its way to the top military commanders and the President of the United States at the time, John F. Kennedy. U.S. leaders were faced with a choice: allow the installations to continue and live with the threat or confront the Soviet government and demand their removal. For 13 tense days negotiations and military readiness for war between the two countries ebbed and flowed. Both sides understood the ramifications of a nuclear attack but diplomatic negotiations had not produced a scenario where each side could save face.
The U.S. navy played a key role during this crisis. On the surface, the Navy carried out the President s order to quarantine missiles and associated supplies from reaching Cuba, essentially a blockade, preventing the components for completion of the missile sites from reaching the island nation. Under the sea, Navy submarines patrolled the oceans ready to launch nuclear missiles at the Soviet Union if a war broke out. Their unknown locations insured that attacks from the Soviet Union would not likely stop the submarine threat before a retaliatory strike could be carried out in defense of the United States. While there was a recurring belief that we were right on the brink of nuclear destruction the crisis came to a peaceful outcome. When the Soviet ships faced the U.S. Naval blockade they turned back. As the press reported at the time, the Soviet Union and its leader, Nikita Khrushchev, blinked. Shortly after that point, the missile bases were taken apart and shipped back to the Soviet Union. U.S. Airborne photography confirmed the presence of the missiles and the missile launchers on ships sailing from Cuba. In return for removal of the missiles the United States agreed not to invade Cuba. The release of classified documents released many years later revealed that the two nations were much closer to nuclear war than was even reported in the press. Direct communication had been carried out between President Kennedy and Premier Khrushchev, a level of negotiations unheard of, in an effort to avert war. It was also revealed that the United States had agreed to remove missile bases located in Turkey which were a threat to the Soviet Union, but at a later time so that the events would not appear to be connected. It was a negotiating concession that allowed both sides to report victory. Resources: The Cuban Missile Crisis: Videos (produced for 50 th by NHF): and http://www.youtube.com/watch?v=ckuws9e-flo&feature=plcp Written: http://www.jfklibrary.org/jfk/jfk-in-history/cuban-missile-crisis.aspx and https://www.history.navy.mil/content/dam/nhhc/research/publications/publication-pdf/cordonofsteel.pdf by Curtis A. Utz.
Projectile motion explanation, formulas, and practice problems: http://www.physics247.com/physics-homework-help/projectile-motion.php The 6 ballistic missiles used by the U.S. Navy during the Cold War: Instructions: Activity One is for a basic physics class with simplified math. All launches take place at the optimum launch angle of 45 degrees where the distance initially travelled along the x and y axis are the same and can be solved using the Pythagorean Theorem (a 2 + b 2 = c 2 ) instead of basic trig. Activity Two integrates Common Core State Standards in English Language Arts and Social Studies into a discussion and literacy activity to introduce students to the ramification of historical events associated with the Cuban Missile Crisis during the Cold War.
Activity One Missiles Away Basic Physics Objective: Students will solve projectile motion problems by determining how far away a U.S. nuclear submarine could launch its missiles and still hit the target. Students will see how advances in technology allowed Navy submarines to patrol closer and closer to home as newer missiles extended the maximum effective range. Materials: Student Handout for activity, compass-pencil, calculators Instructions: Students are provided operational characteristics for six different submarine launched ballistic missiles and asked to calculate the maximum range of the missile by examining the missile s movement along the x and y axis. This activity is for a basic physics class with simplified math. All launches take place at the optimum launch angle of 45 degrees. The acceleration phase of the solid rocket boosters is complete, and the initial velocity of the missile is provided to the student. NOTE: Activity Two integrates Common Core State Standards for English Language Arts and Social Studies into a discussion and literacy activity to introduce students to the ramification of historical events associated with the Cuban Missile Crisis during the Cold War.
Activity 1: Missiles Away Technology advances in missile design provided six different nuclear-tipped ballistic missiles for use in Navy ballistic missile submarines during the Cold War. Each one was more powerful and went further than its predecessor. This increased range changed the areas where American submarines patrolled. Given their calculations of maximum range for each missile, students are to determine where on the Atlantic Ocean a submarine could be and still land a missile on target on Moscow. Students will need a compass to draw a semi-circle to estimate the maximum -range of locations the submarine could launch from. Answer the questions and compare results of your patrol area plot (map at end of activity) (Graphing Hint: To compensate for the curve of the earth the circles will be draw around London. Subtract the 2500 km distance from London to Moscow from your missile range and then use the remaining distance to plot your semi-circle submarine patrol location from London). Distance: New York to London = 5,600 Km London to Moscow = 2,500 Km US Navy Submarine Nuclear Ballistic Missiles Type of Entered Launch Initial Velocity in missile service angle Km/sec Polaris A1 1960 45 o 2.30 Polaris A2 1962 45 o 2.60 Polaris A3 1964 45 o 3.36 Poseidon 1972 45 o 3.36 Trident C4 1979 45 o 4.25 Trident D5 1990 45 o 5.25 Initial Velocity in Km/hour Range in Km Plot you range calculations on the map. Remember to subtract the distance between Moscow and London and then draw your distance semi- circle with London as the starting point.
Questions: What was a major disadvantage of the Polaris A1 missile? What advantage did the submarine fleet gain when the Polaris A2 replaced the Polaris A1? If three missiles have the same range what would be a strategic reason to upgrade? Given three missiles had the same range, what changed in the mathematical relationship between acceleration and time? Why would the weapons designers want to do that? What strategic advantage did the new Trident D5 provide for U.S. Navy submarines? (Hint: the distance from Moscow to Anchorage is 7,025 Km.)
Activity 2 At the Height of the Cold War The Cuban Missile Crisis Objective This lesson integrates Common Core State Standards for English Language Art and Social Studies into a discussion and literacy activity to introduce students to the ramification of historical events associated with the Cold War. Materials: Class set of the attached article, Cordon of Steel, for student use, or on-line link: https://www.history.navy.mil/content/dam/nhhc/research/publications/publication-pdf/cordonofsteel.pdf by Curtis A. Utz. Optional show videos on the Cuban missile crisis: http://www.youtube.com/watch?v=ckuws9e-flo&feature=plcp Instructions: Students will read the handout with the article on the Cuban Missile Crisis and/or watch the prepataory videos, then provide written answers to a set of questions. These will be collected for evaluation at the end of the period to assess proficiency of CCSS ELA standards by the students. If time permits, a second class period could be devoted to a class discussion of the essay and other questions related to the Cuban Missile Crisis, and its relation to current 21 st century events...questions for the students to answer in writing after reading the article: 1. What changes came about in United States Soviet relations as a result of the Cuban Missile Crisis? 2. How did President Kennedy describe the changes in relations between the two nations? Explain what he wanted the average American to conclude from his message. 3. What reasons would support the escalation of the arms race even as the missile crisis ended? 4. Speculate: You know what was happening at the top level of the United States government during the Cuban Missile Crisis. Develop a story for what you think was happening in Moscow between Khrushchev and the top Russian leaders at the same time? Optional homework: What research can you find on the internet that supports your scenario? Share your finding with the class.
Activity One: Missiles Away (ANSWERS) Distance: New York to London = 5,600 Km London to Moscow = 2,500 Km US Navy Submarine Nuclear Ballistic Missiles Type of Entered Launch Initial Velocity V in Initial Velocity in missile service angle Km/hr Km/sec Polaris A1 1960 45 o 2.30 8280 2159 Polaris A2 1962 45 o 2.60 9360 2759 Polaris A3 1964 45 o 3.36 12096 4608 Poseidon 1972 45 o 3.36 12096 4608 Trident C4 1979 45 o 4.25 15300 7372 Trident D5 1990 45 o 5.25 18900 11250 Range in Km 4V 2 / 9.8 m/s 2 Plot you range calculations on the map. Remember to subtract the distance between Moscow and London and the draw you distance semi- circle with London as the starting point. SOLUTION: V y = 0 V y V x X
The time of flight times the horizontal velocity will provide the estimated distance X travelled by the projectile: X = V x t flight where V x = constant = initial x- velocity and t flight = t up + t down Using the 45 degree launch angle, V x = V y = initial velocity x sin 45 = V x 0.707 for each launch. Also, at the peak of the parabolic trajectory, V y = 0 where V y = initial velocity gt where g = 9.8 m/s 2 Therefore solving for t up = t peak = initial y- velocity /9.8 m/s 2 and then t flight = t up + t down = 2(initial y- velocity /9.8 m/s 2 ) To calculate the Range, combine all terms: X = V x t flight = V x times 2 t peak (see table for range calculation solutions) X = (V x 0.707) (2)(V x 0.707)/9.8m/s 2 X = 4V 2 / 9.8 m/s 2
Questions: What was a major disadvantage of the Polaris A1 missile? The Polaris A1 missile was first launched on 20 July 1960 from USS George Washington (SSBN598) while cruising submerged off the coast of Cape Canaveral, Florida. It went on its first operational patrol on 15 November, 1960. The missile remained operational until 14 October 1965. Its major disadvantage was the relatively short range, 1200 nautical miles (1380 statute miles), requiring the ballistic missile submarine carrying the Polaris A1 to remain relatively close to the coast for the missile to be in range of potential targets on land. That can clearly be seen on the chart of possible missile patrol areas. What advantage did the submarine fleet gain when the Polaris A2 replaced the Polaris A1? The Polaris A2 missile was first launched on 23 October 1961 from USS Ethan Allan (SSBN 608) while cruising submerged off the coast of Cape Canaveral, Florida. It went on its first operational patrol on 26 June 1962. The advantage gained was a longer range: 1500 nautical miles (1730 statute miles), a 25% improvement. Compared to the Polaris A1 (28,000 pounds), the Polaris A2 weighted 32,500 pounds. The longer range provided a much larger patrol area for the submarine. The larger patrol area provided for greater security and less chance of being detected, maintaining the strategic deterrence value of the ship. If three missiles have the same range what would be a strategic reason to upgrade? Upgrades would be done to the missiles to: 1. Increase the number of warheads the missile could carry. 2. Increase the accuracy of the guidance system to ensure target coverage with fewer missiles. 3. Increase the range of the missile to cover more targets or have larger, more secure patrol areas. (The Polaris A3 with a range of 2500 nautical miles (2880 statute miles) and 35,700 pound weight, left NO land target inaccessible to the missile_ 4. Improve the fuel to provide for a longer missile lifetime (economic reason).
Given three missiles had the same range, what changed in the mathematical relationship between acceleration and time? Why would the weapons designers want to do that? To achieve the same speed and therefore same range, as the missiles increased in size and weight to include more warheads, the mass of the missiles increased due to warheads and fuel. Therefore, to maintain the range, the missile would have to provide thrust (force) for a longer period of missile burn time, provide a greater overall thrust (force), or both since: acceleration = Force/Mass (Newton s Second Law of Motion) and velocity = acceleration x time of missile burn and distance = velocity x time of flight. What strategic advantage did the new Trident D5 provide for U.S. Navy submarines? (Hint: the distance from Moscow to Anchorage is 7,025 Km.) The advantages included: 1. Longer range (more than 4000 nautical miles) 2. More warheads 3. Improved accuracy 4. Larger patrol areas (the D5 missile could target Moscow from Pacific Ocean patrol areas).
Activity 2: At The Height of the Cold War, The Cuban Missile Crisis (Answers) Questions for the students to answer in writing after reading the article: 1. What changes came about in United States Soviet relations as a result of the Cuban Missile Crisis? Separate from the issue of missiles (the Soviets removed theirs from Cuba, we removed ours from Turkey), the proximity of the flashpoint for a nuclear conflict caused serious reflection on the U.S. Cold War posture and timely communications by our leadership. President Kennedy urged Americans to reexamine Cold War stereotypes and myths and called for a strategy of peace that would make the world safe for diversity, in a commencement address at American University in Washington DC. Two additional actions also signaled a warming in relations between the superpowers: the establishment of a teletype "Hotline" between the Kremlin and the White House and the signing of the Limited Nuclear Test Ban Treaty on July 25, 1963. 2. How did President Kennedy describe the changes in relations between the two nations? Explain what he wanted the average American to conclude from his message. In contrast with language very different from his inaugural address in 1961, President Kennedy told Americans in June 1963, "For, in the final analysis, our most basic common link is that we all inhabit this small planet. We all breathe the same air. We all cherish our children's future. And we are all mortal." From this, he desired the average American to understand that our Nation needed to work toward peaceful solutions, while at the same time deterring conflict with the Soviet Union, because it could escalate into earth- destroying consequences. 3. What reasons would support the escalation of the arms race even as the missile crisis ended? During the crisis, U.S. nuclear superiority was readily apparent to the Soviet Union. At 1900 on 22 October, the Joint Chiefs set Defense Condition 3 for all U.S. forces worldwide. Polaris submarines moved to their launch points. SAC B- 52s and other bombers, fully armed with nuclear bombs, went on alert at dispersal fields in the United States and overseas. SAC also fueled and readied for launching over 100 ICBMs. All these weapons were designated to strike targets in the Soviet Union and Eastern Europe.
Not only were the Polaris submarines virtually invisible and invulnerable as they awaited launch orders under many fathoms of ocean water, but they could maneuver close to the enemy homeland before unleashing their terrible weapons. The existence and readiness of this strategic arsenal clearly helped President Kennedy dissuade the Soviets from brandishing their much weaker nuclear sword. As a result, to attempt to achieve parity with the U.S nuclear and naval forces, the Soviet Union escalated their nuclear and naval arms development after the crisis ended. The Soviet leaders did not want to be be placed in a position of weakness in a potential future Cold War confrontation due to a disadvantage in arms. 4. Speculate: You know what was happening at the top level of the United States government during the Cuban Missile Crisis. Develop a story for what you think was happening in Moscow between Khrushchev and the top Russian leaders at the same time? Optional homework: What research can you find on the internet that supports your scenario? Share your finding with the class. Areas of weakness of the Soviet Union compared to the U.S. that might be discussed by Russian leaders: U.S. nuclear and naval forces were superior, valuable not only for deterring nuclear or conventional conflict, but for enabling President Kennedy to manage the crisis without resorting to aggression. The fleet s presence on the seaward approaches to Cuba placed the onus of any military escalation on the Soviets. The USA did not need the permission of any multinational organization or single nation to deploy these forces. The strength and effectiveness of the U.S. naval quarantine made it militarily and politically acceptable for member states of the OAS to join the effort. Freedom of the sea also allowed Canadian and British naval units to take part in the surveillance effort without negotiating a political agreement. The U.S. and NATO fleet was able to remain on station Independence operated for 54 days at sea because of continuous replenishment by naval logistic ships. This capability made it possible for the president to mount and maintain the de facto blockade.