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A person of mass 72 kg sitting on ice pushes a block of mass of 30kg on ice horizontally with a speed of $12 {ms}^{- 1}$ . The coefficient of friction between the man and ice and between block and ice in 0.02. If $g = 10 {ms}^{- 2}$ , the distances between man and the block, when they come to rest is

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350 m

422.5 m

10 m

360 m

answer is D.

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Detailed Solution

m = 72 kg, P_{i} = P_{t}

$0 = 30 \times 12 + 72 \times v$

$30 \times 12 = - 72v$

$v = 5 m/s$

$a_{m} = \frac{F}{m}$

$= \frac{0.02 \times 72 \times 10}{72} = 0.2$

$a_{b} = μ_{k} g$

$= 0 .02 \times 10 = 0 .2$

$0 - 144 - 2 (0.2) S_{1}$

$S_{2} = 360$

$- 25 = 2 \times (- 0.2) S_{1}$

$S_{1} = 62.5$

$S_{1} + S_{2} = 360 + 62.5 = 422.5 m$

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