NUMERICALS

The magnitudes of two mutually perpendicular vectors $\overrightarrow{P}$ and $\overrightarrow{Q}$ are $5$ and $7$ respectively. Find the magnitude of $\overrightarrow{P}+\overrightarrow{Q}$ and $\overrightarrow{P}-\overrightarrow{Q}$.

A car is going towards north with a velocity $20 m{s}^{-1}$.  After some time it starts to go towards south with velocity $20 m{s}^{-1}$. Determine change in the velocity of the car.

The velocity of a particle moving on a circular path is $5 cm{s}^{-1}$ towards north at any instant. After traversing one-fourth of the path its velocity is $5 cm{s}^{-1}$ towards east. Indicate the change in velocity in a vector diagram.

A river flows at $3 \mathrm{m}/\sec$ and $300 \mathrm{m}$ wide A man swims across the river with velocity $2 \mathrm{m}/\sec$ directed always perpendicular to flow of current. In what direction does he actually move relative to the shore.

A $300 \mathrm{m}$ wide river flows with a speed of $3 \mathrm{m}/\mathrm{s}$. A man swims across the river with a velocity of $2 \mathrm{m}/\sec$ directed always perpendicular to the flow of current. How far down the stream (from the starting point) does he reach the opposite bank?

A river flows due north with a velocity of $3 \mathrm{km}/\mathrm{h}$. A man rows a boat across river with a velocity of $4 \mathrm{km}/\mathrm{h}$ relative to water due east. What is his velocity relative to the earth?

A river flows due north with velocity of $3 \mathrm{km}/\mathrm{h}$. A man rows a boat across the river with a velocity of $4 \mathrm{km}/\mathrm{h}$ relative to water due east. If river is $1 \mathrm{km}$ wide, how far north of his starting point will he reach the opposite bank.

A river flows due north with a velocity of $3 \mathrm{km}/\mathrm{h}$ . A man rows a boat across the river with velocity of $4 \mathrm{km}/\mathrm{h}$ relative to water due east. How long a time is required to cross the river.