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Q.

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

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a

95m

b

86.6m

c

110m

d

100m

answer is A.

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Detailed Solution

h_{0} = 80 m, T = 6 sec, g = 10 {m/s}^{2}

$T = \sqrt{\frac{{2h}_{o}}{g}} (\frac{1 + e}{1 - e})$

$6 = \sqrt{\frac{2 \times 80}{10}} (\frac{1 + e}{1 - e})$

$6 = 4 (\frac{1 + e}{1 - e})$

$\frac{1 + e}{1 - e} = \frac{3}{2}$

$2 + 2 e = 3 - 3 e$

$5e = 1$

$e = 0 .2$

$H = h (\frac{1 + e^{2}}{1 - e^{2}})$

$= 80 (\frac{1 + 0.04}{0.96})$

$= 86.6 m$

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A body is dropped from a height of 80m 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 = 10 ms−2)