Question

a ship moving with constant velocity, a boy runs 100m, first along the direction of ship in time $T_1$, and second in opposite direction of ship in time $T_2$. Then :

• A. $T_1=T_2$
• B. $T_1>T_2$
• C. $T_1<T_2$
• D. insufficient data

Answer 1

Answer: (C)

T_1 < T_2

Answer 2

The boy's speed relative to the ground is $v_s + v_b$ when running with the ship and $|v_s - v_b|$ when running against it. Since $v_s + v_b$ is always greater than $|v_s - v_b|$ (for non-zero speeds of ship and boy), the boy's effective speed relative to the ground is higher when running with the ship. As time is inversely proportional to speed for a fixed distance, the time taken will be less when the speed is higher. Therefore, $T_1 < T_2$.