Search any question & find its solution
Question:
Answered & Verified by Expert
On a long horizontally moving belt, a child runs to and fro with a speed of $9 \mathrm{~km} / \mathrm{h}$ (w.r.t. belt) between his father and mother located $50 \mathrm{~m}$ apart on the moving belt. The belt moves with a speed of $4 \mathrm{kmh}^{-1}$. For an observer on a stationary platform outside, what is the
(a) speed of the child running in the direction of motion of the belt?
(b) speed of the child running opposite to the direction of motion of the belt? and
(c) time taken by the child in case (a) and (b)? Which of the answers alter if motion is viewed by one of the parents ?
(a) speed of the child running in the direction of motion of the belt?
(b) speed of the child running opposite to the direction of motion of the belt? and
(c) time taken by the child in case (a) and (b)? Which of the answers alter if motion is viewed by one of the parents ?
Solution:
1529 Upvotes
Verified Answer
Let us consider left to right to be the positive direction of $x$-axis.
(a) Here, velocity of belt, $v_{\mathrm{B}}=+4 \mathrm{~km} / \mathrm{h}$
Speed of the child w.r.t. belt, $v_{\mathrm{C}}=+9 \mathrm{~km} / \mathrm{h}$
Speed of the child w.r.t. stationary observer, while running in direction of motion of the belt $v_C^{\prime}=v_C+\mathrm{v}_B=9+4=13 \mathrm{~km} / \mathrm{h}$
(b) Here, $v_B=+4 \mathrm{~km} / \mathrm{h} ; \quad v_C=-9 \mathrm{~km} / \mathrm{h}$
Speed of the child w.r.t. stationary observer, while running in opposite direction of motion of belt $v_C^{\prime}=v_C+v_B=-9+4=5 \mathrm{~km} / \mathrm{h}$
$\therefore \quad$ Velocity of the child in any direction (from father to mother or from mother to father) will be $9 \mathrm{kmh}^{-1}$
or $\frac{5}{2} \mathrm{~ms}^{-1}$.
$\therefore \quad$ Time taken by the child in each case (a) and (b) each is $\mathrm{t}=50 /(5 / 2)=20 \mathrm{~s}$
If the motion is observed by one of the parents, answer to case (a) or case (b) will get altered. It is so because speed of child w.r.t. either of mother or father is $9 \mathrm{~km} / \mathrm{h}$
But answer (c) remains unaltered due to the fact that parents and child are on the same belt and as such all are equally affected by the motion of belt.
(a) Here, velocity of belt, $v_{\mathrm{B}}=+4 \mathrm{~km} / \mathrm{h}$
Speed of the child w.r.t. belt, $v_{\mathrm{C}}=+9 \mathrm{~km} / \mathrm{h}$
Speed of the child w.r.t. stationary observer, while running in direction of motion of the belt $v_C^{\prime}=v_C+\mathrm{v}_B=9+4=13 \mathrm{~km} / \mathrm{h}$
(b) Here, $v_B=+4 \mathrm{~km} / \mathrm{h} ; \quad v_C=-9 \mathrm{~km} / \mathrm{h}$
Speed of the child w.r.t. stationary observer, while running in opposite direction of motion of belt $v_C^{\prime}=v_C+v_B=-9+4=5 \mathrm{~km} / \mathrm{h}$
$\therefore \quad$ Velocity of the child in any direction (from father to mother or from mother to father) will be $9 \mathrm{kmh}^{-1}$
or $\frac{5}{2} \mathrm{~ms}^{-1}$.
$\therefore \quad$ Time taken by the child in each case (a) and (b) each is $\mathrm{t}=50 /(5 / 2)=20 \mathrm{~s}$
If the motion is observed by one of the parents, answer to case (a) or case (b) will get altered. It is so because speed of child w.r.t. either of mother or father is $9 \mathrm{~km} / \mathrm{h}$
But answer (c) remains unaltered due to the fact that parents and child are on the same belt and as such all are equally affected by the motion of belt.
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.