(a) What is the initial total mechanical energy of the projectile? J (b) Suppose

Question

(a) What is the initial total mechanical energy of the projectile?
J

(b) Suppose the projectile is traveling 90.7 m/s at its maximum height of y = 309 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

A 56.0-kg projectile is fired at an angle of 30.0 above the horizontal with an initial speed of 1.28 x 10^2 m/s from the top of a cliff 138 m above level ground, where the ground is taken to be y = 0. (a) What is the initial total mechanical energy of the projectile? J (b) Suppose the projectile is traveling 90.7 m/s at its maximum height of y = 309 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 = KE + PE = 1/2 mv^2 + m g y = 0.5*56*128^2 + 56*9.81*138= 5.35E5 J

b) E at max height = 0.5*56*90.7^2 + 56*9.81*309=4.0E5 J

W = dE = 4.0E5 - 5.35E5 = -1.35E5 J

c)

W = dE
Efinal = 1/2 mv^2
1.5*-1.35E5 = 0.5*56*v^2 - 4.0E5

v=84.0 m/s

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