Embibe Experts Solutions for Chapter: Kinematics, Exercise 1: BITSAT 2017

A projectile is given an initial velocity of $\left(\hat{\mathrm{i}}+\sqrt{3} \hat{\mathrm{j}}\right) \mathrm{m} {\mathrm{s}}^{-1},$ where $\hat{\mathrm{i}}$ is along the ground and $\hat{\mathrm{j}}$ is along the vertical. Then, the equation of the path of projectile is $[$Take, $\left.g=10 \mathrm{m} {\mathrm{s}}^{-2}\right]$

Consider the acceleration, velocity and displacement of a tennis ball as its falls to the ground and bounces back. Directions of which of these change in the process?

A stone is projected with velocity $2\sqrt{gh}$, so that it just clears two walls of equal height $h$, at distance of $2h$ from each other. The time interval of passing between the two walls is

A ball is dropped vertically from a height $d$ above the ground. It hits the ground and bounces up vertically to a height $d/2.$ Neglecting subsequent motion and air resistance, its velocity $v$ varies with height $h$ above the ground as

An aeroplane is flying in a horizontal direction with a velocity $u$ and at a height of $2000 \mathrm{m}$. When it is vertically below a point $A$ on the ground a food packet is released from it. The packet strikes the ground at point $B$. If $AB=3 \mathrm{km}$ and $g=10 \mathrm{m} {\mathrm{s}}^{-2}$, then the value of $u$ is

The horizontal range and maximum height attained by a projectile are $R$ and $H$ respectively. If a constant horizontal acceleration $a=\frac{g}{4}$ is imparted to the projectile due to wind, then its horizontal range and maximum height will be 

The velocity of a projectile at the initial point $A$ is $\left(2\hat{\mathrm{i}}-3\hat{\mathrm{j}}\right) \mathrm{m} {\mathrm{s}}^{-1}$. Its velocity (in $\mathrm{m} {\mathrm{s}}^{-1}$) at point $B$ is

A particle moving along $X$-axis has acceleration $f$, at time $t$ given by$f=f_0\left(1-\frac{t}{T}\right)$, where $f_0$ and $T$ are constants. The particle at $t=0$ and the instant when $f=0$, the particle's velocity $v_x$ is