Question 24: 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: