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
B
95m
C
100m
D
110m

Solution

## The correct option is A $$86.6$$mLet 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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