An object with a mass of 42.0 kg is fired with an initial speed of 1.32 102 m/s

Question

An object with a mass of 42.0 kg is fired with an initial speed of 1.32 102 m/s at an angle of 30.0° above the horizontal from a 122-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 = 303 m, it is traveling 93.5 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)The intial mech energy of the object would be the sum of its PE and KE

E = PE + KE

E = m g h + 1/2 m v^2 = m (gh + v^2/2)

E = 42 (9.8 x 122 + 132^2/2) = 4.16 x 10^5 J

HEnce, E = 4.16 x 10^5 J

b)E' = m (gh' + v'^2/g)

E' = 42 (9.8 x 303 + 93.5^2/2) = 3.08 x 10^5 J

Work done by the friction is equal to the energy lost

Wf = E - E' = (4.16 - 3.08) x 10^5 = 1.08 x 10^5 J

Hence, Wf = 1.08 x 10^5 J

c)Wf(tot) = 2.5W

E'' = E - 2.5W = (4.16 - 2.5 x 1.08) 10^5 = 1.46 x 10^5 J

at ground, h = 0

1/2 m v^2 = 1.46 x 10^5

v = sqrt (2 x 1.46 x 10^5/42) = 83.38 m/s

Hence, v = 83.38 m/s

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