Question

A ball is gently dropped from a height of 20 m onto a hard surface where it make an elastic collision. If frictional losses are very small, it returns to its original height and continues to bounce up and down.
1) Show that the speed of the ball just before hits the ground is 20m/s (g=10m/s2)

Answer 1

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given :}} \\ \tt: \implies Height = 20 \: m \\ \\ \red{\underline \bold{To \: Show:}} \\ \tt: \implies Speed \: of \: ball \: just \: hits \: the \: ground = 20 \: m/s$

• According to given question :

$\tt \circ \: Initial \: velocity = 0 \: m/s \\ \\ \tt \circ \: Acceleration = 10 { \: m/s}^{2} \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies s = ut + \frac{1}{2 } {at}^{2} \\ \\ \tt: \implies 20 = 0 \times t + \frac{1}{2} \times 10 \times {t}^{2} \\ \\ \tt: \implies 20 = 5 {t}^{2} \\ \\ \tt: \implies {t}^{2} = 4 \\ \\ \green{\tt: \implies t = 2 \: sec} \\ \\ \bold{Again : } \\ \tt: \implies v = u + at \\ \\ \tt: \implies v = 0 + 10 \times 2 \\ \\ \green{\tt: \implies v = 20 \: m/s} \\ \\ \green{\huge {\boxed{ \bold{Verified}}}}$