Embibe Experts Solutions for Chapter: Kinematics, Exercise 2: Exercise - 2

A man is travelling on a flat car which is moving up a plane inclined at $\cos \theta =\frac{4}{5}$ to the horizontal with a speed $5 \mathrm{m} {\mathrm{s}}^{-1}$. He throws a ball towards a stationary hoop located perpendicular to the incline in such a way that the ball moves parallel to the slope of the incline while going through the centre of the hoop. The centre of the hoop is $4 \mathrm{m}$ high from the man's hand calculate the time taken (in $\mathrm{s}$) by the ball to reach the hoop in second. 

A stone is projected horizontally with speed $V$ from a height $h$ above ground. A horizontal wind is blowing in a direction opposite to the velocity of projection and gives the stone a constant horizontal acceleration $f$ (in a direction opposite to the initial velocity). As a result, the stone falls on the ground at a point vertically below the point of projection. Then find the value of $\frac{f^{2}h}{g{V}^2}$.

($g$ is acceleration due to gravity)

If at an instant the velocity of a projectile be $60 \mathrm{m} {\mathrm{s}}^{-1}$ and its inclination to the horizontal be $30°,$ at what time interval (in $\mathrm{s}$) after that instant will the particle be moving at right angles to its former direction. $\left(g=10 \mathrm{m} {\mathrm{s}}^{-2}\right)$

An open tank $10 \mathrm{m}$ long and $2 \mathrm{m}$ deep, is filled up to a height $1.5 \mathrm{m}$of oil of specific gravity$0.80.$ The tank is accelerated uniformly from rest to a speed of $10 \mathrm{m} {\mathrm{s}}^{-1}$. The shortest time (in seconds) in which this speed may be attained without spilling any oil (in sec).$[g=10 \mathrm{m} {\mathrm{s}}^{-2}]$ 

A stone is projected from level ground at $t=0 \mathrm{s}$  such that its horizontal and vertical components of initial velocity are $10 \mathrm{m} {\mathrm{s}}^{-1}$ and $20 \mathrm{m} {\mathrm{s}}^{-1}$, respectively. Then the instant of time at which magnitude of tangential and magnitude of normal components of acceleration of stone are same is (neglect air resistance). (Use $g=10 \mathrm{m} {\mathrm{s}}^{-2}$).

A striker is shot from a square carom board from a point A exactly at midpoint of one of the walls with a speed $2 \mathrm{m}/\sec$ at an angle of $45°$ with the $\mathrm{x}-\mathrm{axis}$as shown. The collisions of the striker with the walls of the fixed carom are perfectly elastic. The coefficient of kinetic friction between the striker and board is $0.2.$ 

In the figure shown all the surface are smooth. All the blocks $A, B$ and $C$ are movable $x$-axis is horizontal and y-axis vertical as shown. Just after the system is released from the position as shown.

Figure shows the displacement of a particle going along the $x$-axis as a function of time. Find the region where force acting on the particle is zero.