A 58.0-kg projectile is fired at an angle of 30.0° above the horizontal with an

Question

A 58.0-kg projectile is fired at an angle of 30.0° above the horizontal with an initial speed of 144 m/s from the top of a cliff 124 m above level ground, where the ground is taken to be

y = 0.

(a) What is the initial total mechanical energy of the projectile? (Give your answer to at least three significant figures.)
J

(b) Suppose the projectile is traveling 102.1 m/s at its maximum height of y = 340 m.

How much work has been done on the projectile by air friction?
J

(c) What is the speed of the projectile immediately before it hits the ground if air friction does one and a half times as much work on the projectile when it is going down as it did when it was going up?
m/s

Explanation / Answer

a) E = m g h + 1/2 m u2

= (58 * 9.8 * 124) + (0.5 * 58 * 1442)

= 671825.6 J

b) E' = m g h + 1/2 m v2

= (58 * 9.8 * 340) + (0.5 * 58 * 102.12) = 495563.9 J

Work done by friction = E' - E = -176261.71 J

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