A ball is thrown vertically upwards with a velocity of 10 $m s^{- 1}$ . It returns to the ground with a velocity
of 9 $m s^{- 1}$ . If g = 9.8 $m s^{- 2}$ , then the maximum height attained by the ball is nearly (assume air resistance
to be uniform)

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4.1 m

5 m

4.61 m

5.1 m

answer is C.

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Detailed Solution

For upward motion, $\frac{1}{2} m (10)^{2} = m g h + R_{α} h$ …(i)

where. R_a = air resistance

For downward motion. $m g h = \frac{1}{2} m (9)^{2} + R_{a} h$ …(ii)

Solving Eqs. (i) and (iii), we get

$2 m g h = \frac{1}{2} m (100 + 81) \Rightarrow h = 4.61 m$

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