Relative velocity — practice questions

Question 1 · difficulty L2 · understanding

Train A is moving along two parallel rail tracks towards north with speed $$72 \mathrm{~km} / \mathrm{h}$$ and train B is moving towards south with speed $$108 \mathrm{~km} / \mathrm{h}$$. Velocity of train B with respect to A and velocity of ground with respect to B are (in $$\mathrm{ms}^{-1}$$):

• A. -50 and -30
• B. -50 and 30
• C. -30 and 50
• D. 50 and -30

Question 2 · difficulty L2 · understanding

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:

• A. 80 m
• B. 200 m
• C. 120 m
• D. 320 m

Question 3 · difficulty L2 · understanding

Two buses P and Q start from a point at the same time and move in a straight line and their positions are represented by $${X_P}(t) = \alpha t + \beta {t^2}$$ and $${X_Q}(t) = ft - {t^2}$$. At what time, both the buses have same velocity?

• A. $${{\alpha - f} \over {1 + \beta }}$$
• B. $${{\alpha + f} \over {2(\beta - 1)}}$$
• C. $${{\alpha + f} \over {2(1 + \beta )}}$$
• D. $${{f - \alpha } \over {2(1 + \beta )}}$$

Question 4 · difficulty L2 · understanding

A boy reaches the airport and finds that the escalator is not working. He walks up the stationary escalator in time t 1 . If he remains stationary on a moving escalator then the escalator takes him up in time t 2 . The time taken by him to walk up on the moving escalator will be :

• A. $${{{t_1}{t_2}} \over {{t_2} - {t_1}}}$$
• B. $${{{t_1} + {t_2}} \over 2}$$
• C. $${{{t_1}{t_2}} \over {{t_2} + {t_1}}}$$
• D. $${t_2} - {t_1}$$

Question 5 · difficulty L2 · understanding

The position vector of a moving body at any instant of time is given as $\overrightarrow{\mathrm{r}}=\left(5 \mathrm{t}^2 \hat{i}-5 \mathrm{t} \hat{j}\right) \mathrm{m}$. The magnitude and direction of velocity at $t=2 s$ is,

• A. $5 \sqrt{17} \mathrm{~m} / \mathrm{s}$, making an angle of $\tan ^{-1} 4$ with - ve Y axis
• B. $5 \sqrt{15} \mathrm{~m} / \mathrm{s}$, making an angle of $\tan ^{-1} 4$ with + ve $X$ axis
• C. $5 \sqrt{17} \mathrm{~m} / \mathrm{s}$, making an angle of $\tan ^{-1} 4$ with + ve $X$ axis
• D. $5 \sqrt{15} \mathrm{~m} / \mathrm{s}$, making an angle of $\tan ^{-1} 4$ with $-$ ve $Y$ axis

Question 6 · difficulty L2 · understanding

Position of an ant ($$\mathrm{S}$$ in metres) moving in $$\mathrm{Y}$$-$$\mathrm{Z}$$ plane is given by $$S=2 t^2 \hat{j}+5 \hat{k}$$ (where $$t$$ is in second). The magnitude and direction of velocity of the ant at $$\mathrm{t}=1 \mathrm{~s}$$ will be :

• A. $$16 \mathrm{~m} / \mathrm{s}$$ in $$y$$-direction
• B. $$4 \mathrm{~m} / \mathrm{s}$$ in $$x$$-direction
• C. $$9 \mathrm{~m} / \mathrm{s}$$ in $$\mathrm{z}$$-direction
• D. $$4 \mathrm{~m} / \mathrm{s}$$ in $$y$$-direction

Question 7 · difficulty L2 · understanding

At time $$t=0$$ a particle starts travelling from a height $$7 \hat{z} \mathrm{~cm}$$ in a plane keeping z coordinate constant. At any instant of time it's position along the $$\hat{x}$$ and $$\hat{y}$$ directions are defined as $$3 \mathrm{t}$$ and $$5 \mathrm{t}^{3}$$ respectively. At t = 1s acceleration of the particle will be

• A. $$-30 \hat{y}$$
• B. $$30 \hat{y}$$
• C. $$3 \hat{x}+15 \hat{y}$$
• D. $$3 \hat{x}+15 \hat{y}+7 \hat{z}$$

Question 8 · difficulty L2 · understanding

The speed of a swimmer is $$4 \mathrm{~km} \mathrm{~h}^{-1}$$ in still water. If the swimmer makes his strokes normal to the flow of river of width $$1 \mathrm{~km}$$, he reaches a point $$750 \mathrm{~m}$$ down the stream on the opposite bank. The speed of the river water is ___________ $$\mathrm{km} ~\mathrm{h}^{-1}$$

Question 9 · difficulty L2 · understanding

A swimmer wants to cross a river from point A to point B. Line AB makes an angle of 30$$^\circ$$ with the flow of river. Magnitude of velocity of the swimmer is same as that of the river. The angle $$\theta$$ with the line AB should be _________$$^\circ$$, so that the swimmer reaches point B.

Question 10 · difficulty L2 · understanding

A person is swimming with a speed of 10 m/s at an angle of 120$$^\circ$$ with the flow and reaches to a point directly opposite on the other side of the river. The speed of the flow is 'x' m/s. The value of 'x' to the nearest integer is __________.