A truck moving on a horizontal road towards t | vedclass

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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?

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