Question 27: Motion in 1D

Question

A passenger sitting in a train A moving at $90 \mathrm{~km} / \mathrm{h}$ observes another train $\mathrm{B}$ moving in the opposite direction for $8 \mathrm{~s}$. If the velocity of the train B is $54 \mathrm{~km} / \mathrm{h}$, then length of train B is:

Accepted Answer

To find the length of train B, we first need to determine the relative velocity between train A and train B. Since they are moving in opposite directions, their velocities add up:
$v_{AB} = v_A + v_B = 90 \mathrm{~km/h} + 54 \mathrm{~km/h} = 144 \mathrm{~km/h}$
Now, we need to convert this relative velocity to meters per second:
$v_{AB} = \frac{144 \mathrm{~km/h} ÃÂ 1000 \mathrm{~m/km}}{3600 \mathrm{~s/h}} = 40 \mathrm{~m/s}$
The passenger in train A observes train B for 8 seconds. To find the length of train B, we can use the formula:
$	ext{length} = 	ext{relative velocity} ÃÂ 	ext{time}$
$	ext{length} = 40 \mathrm{~m/s} ~ÃÂ~ 8 \mathrm{~s} = 320 \mathrm{~m}$
So, the length of train B is 320 meters.

Answer

80 m

Answer

200 m

Answer

120 m

Answer

320 m

Motion in 1D

A passenger sitting in a train A moving at 90 \mathrm{~km} / \mathrm{h} observes another train \mathrm{B} moving in the opposite direction for 8 \mathrm{~s}. If the velocity of the train B is 54 \mathrm{~km} / \mathrm{h}, then length of train B is:

Choose the correct answer: