A ball A is thrown up vertically with a speed u and at the same instant another ball B is released from a height h. At time t, the speed of A relative to B is

Question

A ball A is thrown up vertically with a speed u and at the same instant another ball B is released from a height h. At time t, the speed of A relative to B is (A)  u  (B)  2u  (C)  u-gt  (D)  √(u2-gt)

Tardigrade Admin · Accepted Answer

From equation of motion, we have v=u+gt where u is initial velocity and t is time. For ball A, vA=u-gt For ball B, vB=0+gt ∴ Relative speed, Δ v=vA-vB =(u-gt) hatj-(-gt hatj) =u hatj

Q. A ball $A$ is thrown up vertically with a speed $u$ and at the same instant another ball $B$ is released from a height $h$ . At time $t$ , the speed of $A$ relative to $B$ is

$u$

$2 u$

$u - g t$

$(u^{2} - g t)$

$g t$

From equation of motion,
we have $v = u + g t$
where u is initial velocity and t is time.
For ball A, $v_{A} = u - g t$
For ball B, $v_{B} = 0 + g t$
$∴$ Relative speed, $Δ v = v_{A} - v_{B}$
$= (u - g t) \hat{j} - (- g t \hat{j})$
$= u \hat{j}$

Q. A ball A is thrown up vertically with a speed u and at the same instant another ball B is released from a height h. At time t, the speed of A relative to B is

u

2u

u−gt

(u2−gt)​

gt

From equation of motion, we have v=u+gt where u is initial velocity and t is time. For ball A, vA​=u−gt For ball B, vB​=0+gt ∴ Relative speed, Δv=vA​−vB​ =(u−gt)j^​−(−gtj^​) =uj^​