A truck moving on a horizontal road towards t | vedclass

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

Question

(A) Let the east direction be positive $(+)$ and the west direction be negative $(-)$.Let the mass of the truck be $M$ and the mass of the ball be $m$

Vedclass · Accepted Answer

$65\, ms^{-1}$ towards the east

Vedclass · Answer

(A) Let the east direction be positive $(+)$ and the west direction be negative $(-)$.Let the mass of the truck be $M$ and the mass of the ball be $m$. Since the ball is light,$M \gg m$.The initial velocity of the truck is $u_1 = +20\, ms^{-1}$.The initial velocity of the ball is $u_2 = -25\, ms^{-1}$.For an elastic collision,the relative velocity of separation equals the relative velocity of approach.Velocity of approach $= u_1 - u_2 = 20 - (-25) = 45\, ms^{-1}$.Let $v_1$ and $v_2$ be the final velocities of the truck and the ball,respectively.Since $M \gg m$,the velocity of the truck remains practically unchanged,so $v_1 \approx u_1 = 20\, ms^{-1}$.The relative velocity of separation is $v_2 - v_1$.Equating the two: $v_2 - v_1 = 45\, ms^{-1}$.Substituting $v_1 = 20\, ms^{-1}$:$v_2 - 20 = 45$$v_2 = 65\, ms^{-1}$.Since the result is positive,the ball moves towards the east with a velocity of $65\, ms^{-1}$.

$A$ truck moving on a horizontal road towards the east with a velocity of $20\, ms^{-1}$ collides elastically with a light ball moving with a velocity of $25\, ms^{-1}$ towards the west. What is the velocity of the ball just after the collision?

Similar Questions

Three blocks are initially placed as shown in the figure. Block $A$ has mass $m$ and initial velocity $v$ to the right. Block $B$ with mass $m$ and block $C$ with mass $4m$ are both initially at rest. Neglect friction. All collisions are elastic. The final velocity of block $A$ is

$Assertion$ : In an elastic collision of two billiard balls,the total kinetic energy is conserved during the short time of oscillation of the balls (i.e.,when they are in contact).
$Reason$ : Energy spent against friction does not follow the law of conservation of energy.

$A$ ball falls from a height of $5\,m$ and strikes the roof of a lift. If at the time of collision,the lift is moving in the upward direction with a velocity of $1\,m/s$,then the velocity with which the ball rebounds after collision will be (assume $e = 1$):

Collision takes place between two solid spheres denoted as $1$ and $2$. The initial velocities of the spheres are $u_1 = 3 \ m/s$ and $u_2 = 1.5 \ m/s$,and the final velocities are $v_1 = 2.5 \ m/s$ and $v_2 = 3.5 \ m/s$. The coefficient of restitution between the materials of the spheres is nearly:

Vedclass Test Series

Exam Paper Generator

Online Exam Module