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

The relation between time $t$ and distance $x$ is $t=a{x}^2+bx$, where $a$ and $b$ are constants. The acceleration is:

Two trains, which are moving along different tracks in opposite directions towards each other, are put on the same track due to a mistake. Their drivers, on noticing the mistake, start slowing down the trains when the trains are $300 \mathrm{m}$ apart. Graphs given below show their velocities as a function of time as the trains slow down. What is the separation between the trains (in metre) when both have stopped?

  

Two balls are projected from points $A$ and $B$ in a vertical plane as shown in the figure. $AB$ is a straight vertical line. The balls will collide in mid-air if  $\frac{V_1}{V_2}$ is equal to, 

A stone is released at rest from a height of $45 \mathrm{m}$ above the horizontal level ground. There is horizontal wind blowing due to which stone acquires an additional (in addition to acceleration due to gravity) horizontal acceleration of magnitude $10 \mathrm{m} {\mathrm{s}}^{-2}$. Then the net distance travelled by stone before reaching the ground is (take $g=10 \mathrm{m} {\mathrm{s}}^{-2}$ and neglect air resistance),

In the given figure $AB$ is a pipe fixed to the ground at an inclination of $37°.$ A ball is projected from point $O$ at a speed of $u=20 \mathrm{m}/\mathrm{s}$ at angle of $53°$ to the horizontal and it smoothly enter the pipe with its velocity parallel to the axis of the pipe. Then length of pipe (in metre) is: (Take $g=10{ ms}^{-2}$) (Approximate the answer to the nearest integer.)

A ball is projected at an angle of $30°$ above with the horizontal from the top of a tower and strikes the ground in $5 \mathrm{s}$ at an angle of $45°$ with the horizontal. Find the speed with which it was projected.

Two balls of mass $M$ and $2M$ are thrown horizontally with the same initial velocity $v_0$ from top of a tall tower and experience a drag force of $-kv\left(k>0\right)$ where $v$ is the instantaneous velocity.

Then,