H C Verma Solutions for Chapter: Rest and Motion : Kinematics, Exercise 2: OBJECTIVE I

A motor car is going due north at a speed of $50 \mathrm{km} {\mathrm{h}}^{-1}$. It makes a $90°$ left turn without changing the speed. The change in the velocity of the car is 

A person standing near the edge of the top of a building throws two balls $A$ and $B$. The ball $A$ is thrown vertically upward and $B$ is thrown vertically downward with the same speed. The ball $A$ hits the ground with a speed $v_{\mathrm{A}}$ and the ball $B$ hits the ground with a speed $v_{\mathrm{B}}$. We have

In a projectile motion the velocity

Two bullets are fired simultaneously, horizontally and with different speeds from the same place. Which bullet will hit the ground first?

The range of a projectile fired at an angle of $15°$ is $50 \mathrm{m}$. If it is fired with the same speed at an angle of $45°$, its range in $\mathrm{meters}$ will be

Two projectiles $A$ and $B$ are projected with the angle of projection $15°$ for the projectile $A$ and $45°$ for the projectile $B$. If $R_{\mathrm{A}}$ and $R_{\mathrm{B}}$ be the horizontal range for the two projectiles, then

A river is flowing from west to east at a speed of $5 \mathrm{m} {\min }^{-1}$. A man on the south bank of the river, capable of swimming at $10 \mathrm{m} {\min }^{-1}$ in still water, wants to swim across the river in the shortest time. In which direction should he swim?

In the arrangement shown in the figure, the ends $P$ and $Q$ of an inextensible string move downwards with a uniform speed $u$. Pulleys $A$ and $B$ are fixed. The mass $M$ moves upwards with a speed.