A ball is allowed to fall freely from a heigh | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) When a ball is dropped from a height $H$ and the coefficient of restitution is $e$,the height reached after the first bounce is $h_1 = e^2 H$,afte

Vedclass · Accepted Answer

$58$

Vedclass · Answer

(D) When a ball is dropped from a height $H$ and the coefficient of restitution is $e$,the height reached after the first bounce is $h_1 = e^2 H$,after the second bounce is $h_2 = e^4 H$,and so on.The total distance $D$ travelled by the ball is given by the sum of the initial fall and the infinite series of bounces (up and down):$D = H + 2h_1 + 2h_2 + 2h_3 + ...$$D = H + 2(e^2 H + e^4 H + e^6 H + ...)$$D = H + 2e^2 H (1 + e^2 + e^4 + ...)$Using the sum of an infinite geometric progression $S = \frac{a}{1-r}$,where $a = 1$ and $r = e^2$:$D = H + 2e^2 H \left( \frac{1}{1 - e^2} ight)$$D = H \left( 1 + \frac{2e^2}{1 - e^2} ight) = H \left( \frac{1 - e^2 + 2e^2}{1 - e^2} ight) = H \left( \frac{1 + e^2}{1 - e^2} ight)$Given $H = 42 \ m$ and $e = 0.4$:$e^2 = (0.4)^2 = 0.16$$D = 42 	imes \left( \frac{1 + 0.16}{1 - 0.16} ight) = 42 	imes \left( \frac{1.16}{0.84} ight)$$D = 42 	imes \frac{116}{84} = 42 	imes \frac{116}{2 	imes 42} = \frac{116}{2} = 58 \ m$.

$A$ ball is allowed to fall freely from a height of $42 \ m$ from the ground. If the coefficient of restitution between the ball and the ground is $0.4$,then the total distance travelled by the ball before it comes to rest is (in $m$)

Similar Questions

$A$ ball kept at $20 \,m$ height falls freely in a downward direction vertically and hits the ground. The coefficient of restitution is $0.4$. After the first rebound, the upward velocity is $[g = 10 \,m/s^2]$. (in $\,m/s$)

$A$ sphere of mass $m$ moving with velocity $u$ undergoes a collision with a stationary sphere of mass $m$. If the coefficient of restitution is $e = 1/2$,what is the ratio of the final velocities of the two spheres?

An inelastic ball is dropped from a height of $100\, m$. Due to the impact,$20\%$ of its energy is lost. To what height will the ball rise?

$A$ ball is dropped from a height $h_0$. It undergoes $n$ collisions with the ground. If the velocity of the ball after $n$ rebounds is $u_n$ and it reaches a height $h_n$,which formula gives the coefficient of restitution $e$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module