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A ball is thrown vertically downwards from a height of 20 m with an initial velocity $u_0$. It collides with the ground, loses 50 percent of its energy in collision and rebounds to the same height. The initial velocity $u_0$ is: (Take g = 10 $ms^{-2}$)
A
10 $ms^{-1}$
B
14 $ms^{-1}$
C
20 $ms^{-1}$
D
28 $ms^{-1}$
Detailed Solution
Rebound speed: $v = \sqrt{2gh} = \sqrt{2\times10\times20} = 20$ m/s
Energy just after rebound: $E = \frac{1}{2}mv^2 = 200m$
50% is lost in the collision, so the energy just before collision = 400m.
$\frac{1}{2}mu_0^2 + mgh = 400m \Rightarrow \frac{1}{2}u_0^2 + 200 = 400 \Rightarrow u_0 = 20$ m/s
Energy just after rebound: $E = \frac{1}{2}mv^2 = 200m$
50% is lost in the collision, so the energy just before collision = 400m.
$\frac{1}{2}mu_0^2 + mgh = 400m \Rightarrow \frac{1}{2}u_0^2 + 200 = 400 \Rightarrow u_0 = 20$ m/s