Embibe Experts Solutions for Chapter: Kinematics, Exercise 3: Exercise-3

Two cars travelling towards each other on a straight road at velocity $10 \mathrm{m} {\mathrm{s}}^{-1}$ and $12 \mathrm{m} {\mathrm{s}}^{-1}$ respectively. When they are 150 metre apart, both drivers apply their brakes and each car decelerates at $2 \mathrm{m} {\mathrm{s}}^{-2}$ until it stops. How far apart will they be when they have both come to a stop in meters?

Two trains $A$ and $B$ $100 \mathrm{m}$ and $60 \mathrm{m}$ long are moving in opposite directions on the parallel tracks. The speed of shorter train is $3$ times that of the longer one. If the train take $4$ seconds to cross each other then find the magnitude of ${\overrightarrow{v}}_B-{\overrightarrow{v}}_A$ in $\mathrm{m} {\mathrm{s}}^{-1}$?

A man crosses a river in a boat. If the crosses the river in minimum time he take $10$ minutes with a horizontal drift $120 \mathrm{m}$. If he crosses the river taking shortest path in $12.5$ minutes then find shortest distance for crossing the river in $\mathrm{Km}$.

A projectile is thrown with speed $u$ making angle $\theta$ with horizontal at $t=0$. It just crosses the two points at equal height at time $t=1 \mathrm{s}$ and $t=3 \sec$ respectively. Calculate maximum height attained by it in meter. $\left(g=10 \mathrm{m} {\mathrm{s}}^{-2}\right)$

A food package was dropped from an aircraft flying horizontally. $6 \mathrm{s}$ before it hit the ground, it was at a height of $780 \mathrm{m}$, and had travelled a distance of $1\mathrm{km}$ horizontally. Find the altitude of the aircraft in $\mathrm{km}$.

Two particles are projected from the two towers simultaneously, as shown in the figure. What should be value of '$d$' for their collision in meter.

A particle $A$ moves with velocity $2\hat{i}-3\hat{j}$ from a point $\left(4,5\right)$. At the same instant a particle $B$, moving in the same plane with velocity $4\hat{i}+\hat{j}$ passes through a point $C\left(0,-3\right)$. The $x$ co-ordinate of the point where the particles collide is.

A particle is projected from a point $O$ with an initial speed of $30 \mathrm{m} {\mathrm{s}}^{-1}$ to pass through a point which is $40 \mathrm{m}$ from O horizontally and $10 \mathrm{m}$ above $O$. There are two angles of projection for which this is possible. There angles are $\alpha$ and $\beta$. The value of $\left|\tan \left(\alpha +\beta \right)\right|$ is