When a ball is dropped into a lake from a hei | vedclass

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(B) Step $1$: Calculate the velocity $v$ of the ball when it hits the water surface.Using the equation of motion $v^2 = u^2 + 2gh$,where $u = 0 \, m/s

Vedclass · Accepted Answer

$29.4$

Vedclass · Answer

(B) Step $1$: Calculate the velocity $v$ of the ball when it hits the water surface.Using the equation of motion $v^2 = u^2 + 2gh$,where $u = 0 \, m/s$,$g = 9.8 \, m/s^2$,and $h = 4.9 \, m$:$v^2 = 0 + 2 	imes 9.8 	imes 4.9 = 96.04$$v = \sqrt{96.04} = 9.8 \, m/s$.Step $2$: Calculate the time taken to fall from the height $h$.Using $v = u + gt$:$9.8 = 0 + 9.8 	imes t_1$$t_1 = 1.0 \, s$.Step $3$: Calculate the time taken to sink to the bottom.The total time is $4.0 \, s$,so the time spent in the water is $t_2 = 4.0 - 1.0 = 3.0 \, s$.Step $4$: Calculate the depth of the lake.Since the ball sinks with a constant velocity $v = 9.8 \, m/s$:Depth $= v 	imes t_2 = 9.8 	imes 3.0 = 29.4 \, m$.

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