Question

Two skaters P and Q are skating towards each other. Skater P throws a ball towards Q every $5$s such that it always leaves her hand with speed $2$ $m{s}^{-1}$ with respect to the ground. Consider two cases:
(i) P runs with speed $1$ $m{s}^{-1}$ towards Q while Q remains stationary.
(ii) Q runs with speed $1$ $m{s}^{-1}$ towards P while P remains stationary.
Note that irrespective of speed of P, ball always leaves P's hand with speed $2$ $m{s}^{-1}$ with respect to the ground. Ignore gravity. Balls will be received by Q.

• A. One every $2.5$s in case (I) and one every $3.3$s in case (II)
• B. One every $2$s in case (I) and one every $4$s in case(II)
• C. One every $3.3$s in case (I) and one every $2.5$s in case (II)
• D. One every $2.5$s in case (I) and one every $2.5$s in case (II)

Answer 1

Answer: (A)

One every $2.5$s in case (I) and one every $3.3$s in case (II)

Let the distance between them is x. Time taken by ball to reach is $T_1=\frac{x}{2}$

next ball will be thrown after 5 second, so the distance between P and Q is x-5

$T_2=\frac{x-5}{2}+5$

$T_2-T_2=2.5sec$

Case 2. when Q moves the relative velocity is 2+1=3

$T_1=\frac{x}{3}$

$T_2=\frac{x-5}{3}+5$

$T_2-T_2=3.3$