A ball is thrown vertically downwards from a | vedclass

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

Question

(D) Let $m$ be the mass of the ball,$h = 20 \, m$ be the height,and $v$ be the velocity just before hitting the ground.Using the law of conservation o

Vedclass · Accepted Answer

$20$

Vedclass · Answer

(D) Let $m$ be the mass of the ball,$h = 20 \, m$ be the height,and $v$ be the velocity just before hitting the ground.Using the law of conservation of energy for the downward motion:$\frac{1}{2}mv^2 = \frac{1}{2}mv_0^2 + mgh$$v^2 = v_0^2 + 2gh \quad ... (i)$When the ball hits the ground,it loses $50\%$ of its kinetic energy. The remaining kinetic energy is $\frac{1}{2} 	imes (\frac{1}{2}mv^2) = \frac{1}{4}mv^2$.This remaining energy allows the ball to rebound to the same height $h$:$\frac{1}{4}mv^2 = mgh$$v^2 = 4gh$Substitute $v^2 = 4gh$ into equation $(i)$:$4gh = v_0^2 + 2gh$$v_0^2 = 2gh$$v_0 = \sqrt{2gh}$Given $g = 10 \, m/s^2$ and $h = 20 \, m$:$v_0 = \sqrt{2 	imes 10 	imes 20} = \sqrt{400} = 20 \, m/s$.

$A$ ball is thrown vertically downwards from a height of $20 \, m$ with an initial velocity $v_0$. It collides with the ground,loses $50\%$ of its energy in the collision,and rebounds to the same height. The initial velocity $v_0$ is .................... $m/s$ (Take $g = 10 \, m/s^2$)

Similar Questions

$A$ body of mass $1\,kg$ is thrown upwards with a velocity $20\,m/s$. It momentarily comes to rest after attaining a height of $18\,m$. How much energy is lost due to air friction? (Given $g = 10\,m/s^2$)

Consider the following two statements: $[A]$ The linear momentum of a system is zero. $[B]$ The kinetic energy of the particles of the system is zero.

Two bodies moving towards each other collide and move away in opposite directions. There is some rise in temperature of bodies because a part of the kinetic energy is converted into

$A$ free body of mass $8 \ kg$ is moving at $2 \ m \cdot s^{-1}$ along a straight line. It splits into two equal parts due to an internal explosion releasing $16 \ J$ of energy,and neither part deviates from the original line of motion. What happens to the two parts?

$A$ $2 \, kg$ block is placed on a frictionless inclined plane with an angle of $30^\circ$ and a length of $2 \, m$. After reaching the bottom of the incline,it travels on a surface with a coefficient of friction of $0.25$. What distance (in $m$) will it travel on the surface before coming to rest?

Vedclass Test Series

Exam Paper Generator

Online Exam Module