K K Sharma Solutions for Chapter: Motion in a Plane, Exercise 1: TOPICWISE QUESTIONS

The torque of the force $\overrightarrow{F}=\left(2\hat{\mathrm{i}}-3\hat{\mathrm{j}}+4\hat{\mathrm{k}}\right) \mathrm{N}$ acts at the point $\overrightarrow{r}=\left(3\hat{\mathrm{i}}+2\hat{\mathrm{j}}+3\hat{\mathrm{k}}\right) \mathrm{m}$ about the origin be $\left(\overrightarrow{\tau }=\overrightarrow{r}\times \overrightarrow{F}\right)$

A boy can swim in still water at $1 \mathrm{m} {\mathrm{s}}^{-1}$. He swims across a river flowing at $0.6 \mathrm{m} {\mathrm{s}}^{-1}$ which is $336 \mathrm{m}$ wide. If he travels in the shortest possible time, then what time does he take to cross the river?

A man can swim in still water with a speed of $2 \mathrm{m} {\mathrm{s}}^{-1}$. If he wants to cross a river with water current speed $\sqrt{3} \mathrm{m} {\mathrm{s}}^{-1}$ along the shortest possible path, then in which direction should he swim?

A man wishes to cross a river in a boat. If he crosses the river in minimum time, he takes $10 \min$ with a drift of $120 \mathrm{m}$. If he crosses the river taking the shortest route, he takes $12.5 \min$. Find the velocity of the boat with respect to water.

A boat which has a speed of $5 \mathrm{km} {\mathrm{h}}^{-1}$ in still water crosses a river of width $1 \mathrm{km}$ along the shortest path in $15 \min .$ The velocity of the river water is

A boat is sent (aimed) across (perpendicular) the water flow in a river with a velocity $4 \mathrm{km} {\mathrm{h}}^{-1}$. If the resultant velocity of the boat is $5 \mathrm{km} {\mathrm{h}}^{-1}$, then the velocity of water in the river is

A river $500 \mathrm{m}$ wide is flowing with a current of $5 \mathrm{km} {\mathrm{h}}^{-1}$. A boat starts from one bank of the river, and wishes to cross the river at a right angle to the stream's direction. Boatman can row the boat at $13 \mathrm{km} {\mathrm{h}}^{-1}$. The time he takes to cross the river is

A car is going eastwards with a velocity of $8 \mathrm{m} {\mathrm{s}}^{-1}$. To the passengers in the car, a train appears to be moving northwards with a velocity $15 \mathrm{m} {\mathrm{s}}^{-1}$. What is the actual velocity of the train?