A 50.0 - kg projectile is fired at an angle of 30.0° above the horizontalwith an initial speed of 1.20 x 102 m/s from the top ofa cliff 142 m above level ground, where the ground is taken tobe y = 0. (a) What is the initial total mechanical energy of theprojectile? (b) Suppose the projectile is traveling 85.0 m/s atits maximum height of y = 427 m. How much work has beendone on the projectile by air friction? (c) What is the speed ofthe projectile immediately before it hits the ground if air frictiondoes one and a half times as much work on the projectilewhen it is going down as it did when it was going up?

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Asked Dec 17, 2019
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A 50.0 - kg projectile is fired at an angle of 30.0° above the horizontal
with an initial speed of 1.20 x 102 m/s from the top of
a cliff 142 m above level ground, where the ground is taken to
be y = 0. (a) What is the initial total mechanical energy of the
projectile? (b) Suppose the projectile is traveling 85.0 m/s at
its maximum height of y = 427 m. How much work has been
done on the projectile by air friction? (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?

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Expert Answer

Step 1

(a) Write the expression for initial mechanical energy

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E, = KE, + PE, mv; + - mgy;

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Step 2

Substitute the values

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E, =(50.0 kg)(1.20 x10° m/s) +(50.0 kg)(9.8 m/s² )(142 m) : 4.295 x 10 J 4.30 x 10° J

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Step 3

(b) Write the expression for work done ...

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ΔΚE+ ΔΡΕ W; = AKE + %3D --m(v - ) + mg(y; - 3:)

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Work,Power and Energy

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