An object with a mass of 52.0 kg is fired with an initial speed of 1.34 102 m/s

Question

An object with a mass of 52.0 kg is fired with an initial speed of 1.34 102 m/s at an angle of 30.0° above the horizontal from a 120-m-high cliff (take ground level to be y = 0 m). (a) Determine the initial total mechanical energy of the projectile. J (b) If when the projectile is at its maximum height of y = 307 m, it is traveling 95.0 m/s, determine the amount of work that has been done on the projectile by air resistance. J (c) What is the speed of the projectile immediately before it hits the ground if air resistance 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) TOTAL mechanical energy = PE + KE = mgh + mu^2 /2

= (52 x 9.81 x 120 ) + (52 x 134^2 / 2)

= 528070.4 J

b) using energy conservation,

inital energy + work done by resistance = final energy

528070.4 + Wr = (52 x 9.81 x 307) + (52 x 95^2 /2)

Wr = -136813.56 J

c) total work done by resistance = 2Wr =- 273627.12 J

528070.4 - 273627.12 = 52 x v^2 /2

v = 98.93 m/s

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