An object is dropped from a height h from the | vedclass

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

Question

(A) When the object hits the ground,its kinetic energy becomes $50\%$ of its initial value. Let $v$ be the velocity just before impact and $v'$ be the

Vedclass · Accepted Answer

$3\,h$

Vedclass · Answer

(A) When the object hits the ground,its kinetic energy becomes $50\%$ of its initial value. Let $v$ be the velocity just before impact and $v'$ be the velocity just after impact.$\frac{1}{2}m(v')^2 = \frac{50}{100} 	imes \frac{1}{2}mv^2 \Rightarrow v' = \frac{v}{\sqrt{2}}$.The coefficient of restitution $e$ is defined as $e = \frac{v'}{v} = \frac{1}{\sqrt{2}}$.The total distance $H$ covered by an object dropped from height $h$ undergoing multiple bounces is given by the formula:$H = h + 2h(e^2) + 2h(e^4) + 2h(e^6) + \dots$This is a geometric series: $H = h + 2h \left( \frac{e^2}{1 - e^2} ight) = h \left( \frac{1 - e^2 + 2e^2}{1 - e^2} ight) = h \left( \frac{1 + e^2}{1 - e^2} ight)$.Substituting $e^2 = \frac{1}{2}$:$H = h \left( \frac{1 + 1/2}{1 - 1/2} ight) = h \left( \frac{3/2}{1/2} ight) = 3h$.

An object is dropped from a height $h$ from the ground. Every time it hits the ground,it loses $50\%$ of its kinetic energy. The total distance covered as $t \to \infty$ is

Similar Questions

$A$ body of mass $m_1$ moving with a velocity $3 \, ms^{-1}$ collides with another body at rest of mass $m_2$. After the collision,the velocities of the two bodies are $2 \, ms^{-1}$ and $5 \, ms^{-1}$ respectively along the direction of motion of $m_1$. The ratio $\frac{m_1}{m_2}$ is:

$A$ ball is dropped from a height of $5 \ m$ on a planet. It rebounds to a height of $1.8 \ m$. What is the fraction of velocity lost by the ball?

$A$ ball of mass $M$ falls from a height $h$ on a floor. If the coefficient of restitution is $e$,the height attained by the ball after two rebounds is

$A$ ball of mass $m$ moving with a velocity of $9 \ m/s$ collides with another ball of the same mass $m$ at rest. After the collision,both balls move at an angle of $30^\circ$ with the original direction of motion. Find the velocity $v$ of both balls after the collision. (in $m/s$)

$A$ ball falling freely from a height of $4.9 \, m$ hits a horizontal surface. If the coefficient of restitution is $e = \frac{3}{4}$,then the ball will hit the surface for the second time after .............. $s$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module