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THE PROBLEM On December 6, 1917, a cargo ship carrying explosives collided with

ID: 1790647 • Letter: T

Question

THE PROBLEM On December 6, 1917, a cargo ship carrying explosives collided with another ship in the harbour at Halifax, Nova Scotia. There was a huge explosion. Suppose one small piece of debris was launched straight upward at v=5.2 km/s. Calculate its maximum altitude. PAPER SOLUTION INTERPRET Identify all of the true statements. A. Using g = 9.8 m/s, is sometimes a good approximation B. Newton's law of gravitation is always correct. C. A question of this type never requires Newton's law of gravitation. 7 D. It is difficult to know in advance whether g = 9.8 m/s, is a good approximation for this particular problem. OE. G = 6.67 × 10-11 Nkg-2 m, and g = 9.8 m/s, are related, so both methods are correct. F. A question of this type always requires Newton's law of gravitation. G. None of the above. DEVELOP Derive an algebraic expression for the maximum altitude, assuming the change in potential energy is U = mgh. Derive an algebraic expression for the maximum altitude, using hG

Explanation / Answer

1) using energy conservation,

mgh = 0.5mv^2

h = v^2/2g

hg = v^2/2g

2] again, increase in PE = decrease in KE

-GMm/(R+h) - -GMm/R = 0.5mv^2

GM*(1/R - 1/(R+h)) = v^2/2

(1/R - 1/(R+h)) = v^2/(2GM)   

1/(R+h) = 1/R - v^2/(2GM)

R+ h = 1/(1/R - v^2/(2GM) )

h = 1/(1/R - v^2/(2GM)) - R where R is radius of earth, M is mass of earth

hG = 1/(1/R - v^2/(2GM)) - R