Question

A 2.0 kg mass is projected from the edge of the top of a 20mtall building with a velocity of 24m/s at some unknown angle abovethe horizontal. Disregard air resistance and assume the ground islevel. What is the kinetic energy of the mass just before itstrikes the ground?

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asked 2021-05-10
A 2.0 kg mass is projected from the edge of the top of a 20mtall building with a velocity of 24m/s at some unknown angle abovethe horizontal. Disregard air resistance and assume the ground islevel. What is the kinetic energy of the mass just before itstrikes the ground?

Expert Answers (1)

2021-05-12

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Let the angle of projection be θ and initialvelocity be u \(\displaystyle{m}{s}^{{-{1}}}\).
Initial vertical component of velocity \(\displaystyle={u}{\sin{{0}}}={24}{\sin{{0}}}\)
Horizontaal component of velocity \(\displaystyle={u}{\cos{{0}}}={24}{\cos{{0}}}\)
Eqn. for the vertical component: \(v_{v}^{2} = [(24\sin θ)^{2} +- (2) \times (- 9.8 m s^{-1}) \times (-20 m)]\)

\(=576 \sin^{2}\theta + 392\)

The final horizontal component: \(v_{h}^{2} = 576\cos^{2}\theta\)

K.E. when the 2 kg mass touches the ground =

\((\frac{1}{2}) m[v_{v}^{2} +v_{h}^{2}] = 0.5 \times (2) \times (576\sin^{2}\theta + 392 + 576\cos^{2}\theta)\)

= 968 J

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