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Question

A body is dropped from a height of $$80$$m on to a horizontal floor and impings repeatedly. If it stops in $$6$$ seconds, the total distance travelled by it before stops is (nearly). $$(g=10ms^{-2})$$.


A
86.6m
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B
95m
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C
100m
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D
110m
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Solution

The correct option is A $$86.6$$m
Let the value of coefficient of restitution be $$e$$.
Initial height of the body   $$H = 80 \ m$$
Time taken by the body to reach the ground  $$t = \sqrt{\dfrac{2H}{g}}$$
$$\implies \ t = \sqrt{\dfrac{2\times 80}{10}} = 4 \ s$$
Total time taken by body to stop is given by   $$T = t\bigg(\dfrac{1+e}{1-e}\bigg)$$
$$\therefore \ 6 = 4\bigg(\dfrac{1+e}{1-e}\bigg)$$
$$\implies \ e = 0.2$$
Total distance travelled by body before coming to rest is given by   $$S = H\bigg(\dfrac{1+e^2}{1-e^2}\bigg)$$
$$\therefore$$   $$S = 80\bigg(\dfrac{1+0.2^2}{1-0.2^2}\bigg) = 86.6 \ m$$

Physics

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