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Question
I am writing a story and I would need some information on how much energy would be needed to do these feats.

a) A man throwing a four ton vehicle a dozen meters away in an arch.

b) A man throwing a thirty ton tank a hundred meters away in an arch.

Answer
Hello Mika,

If the objects are thrown with an initial direction 45 degrees above the horizontal, the range will be greatest for any given initial speed, so I will choose that to be the case. I will assume the ton of your question is the metric ton, 1000 kg.

a. The required initial velocity, Vi,is found in the case of the range, R, being 12 m and the launch angle, theta, being 45 degrees using this formula given on this web site:
http://hyperphysics.phy-astr.gsu.edu/hbase/traj.html#tra13:
Vi = sqrt(R*g / sin(2*theta))
where g is the acceleration of gravity: 9.8 m/s^2
Using the data, Vi = sqrt(12 m*(9.8 m/s^2) / sin(2*45)) = 10.84 m/s

Your man gave the vehicle an initial kinetic energy of
KE = (1/2)*m*Vi^2 = (1/2)*4000 kg*(10.84 m/s)^2 = 235,200 Joules

By the principle of conservation of energy, your man had to spend 235,200 Joules to make that throw.

b. Using the same formula and the data m = 30,000 kg and R = 100 m,
Vi = sqrt(100 m*9.8 m/s^2 / sin(2*45)) = 31.30 m/s

Your man gave the tank an initial kinetic energy of
KE = (1/2)*m*Vi^2 = (1/2)*30,000 kg*(10.84 m/s)^2 = 14,700,000 Joules

By the principle of conservation of energy, your man had to spend 14,700,000 Joules to make that throw.

I hope this helps,
Steve

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Steve Johnson

Expertise

I would be delighted to help with questions up through the first year of college Physics. Particularly Electricity, Electronics and Newtonian Mechanics (motion, acceleration etc.). I decline questions on relativity and Atomic Physics. I also could discuss the Space Shuttle and space flight in general.

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I have a BS in Physics and an MS in Electrical Engineering. I am retired now. My professional career was in Electrical Engineering with considerable time spent working with accelerometers, gyroscopes and flight dynamics (Physics related topics) while working on the Space Shuttle. I gave formal classroom lessons to technical co-workers periodically over a several year period.

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BS Physics, North Dakota State University
MS Electrical Engineering, North Dakota State University

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