B M Sharma Solutions for Chapter: Kinematics II, Exercise 78: Archives

A water fountain on the ground sprinkles water all around it. If the speed of water coming out of the fountain is $v$, the total area around the fountain that gets wet is,

A projectile is given an initial velocity of $\hat{\mathrm{i}}+2\hat{\mathrm{j}} \mathrm{m} {\mathrm{s}}^{-1},$ where $\hat{i}$ is along the ground and $\hat{\mathrm{j}}$ is along the vertical. If $g=10 \mathrm{m} {\mathrm{s}}^{-2},$ the equation of its trajectory is

From a tower of height $H,$ a particle is thrown vertically upwards with a speed $u.$ The time taken by the particle, to hit the ground, is $n$ times that taken by it to reach the highest point of its path. The relation between $H, u$ and $n$ is:

Consider a disc rotating in the horizontal plane with a constant angular speed $\omega$ about its centre $O.$ The disc has a shaded region on one side of the diameter and an unshaded region on the other side as shown in the figure. When the disc is in the orientation as shown, two pebbles $P$ and $Q$ are simultaneously projected at an angle towards $R.$ The velocity of projection in the $y-z$ plane and is the same for both pebbles with respect to the disc. Assume that

$\left(\mathrm{i}\right)$ they land back on the disc before the disc has completed $\frac{1}{8}$ rotation,

$\left(\mathrm{ii}\right)$ their range is less than half the disc radius, and

$\left(\mathrm{iii}\right)$ $\omega$ remains constant throughout. Then

A train is moving along a straight line with a constant acceleration $a$. A boy standing in the train throws a ball forward with a speed of $10{ \mathrm{m} \mathrm{s}}^{-1}$ at an angle of $60°$ to the horizontal. The body has to move forward by $1.15 \mathrm{m}$ inside the train to catch the ball back to the initial height. The acceleration of the train, in $\mathrm{m} {\mathrm{s}}^{-2}$ is,

Airplanes $A$ and $B$ are flying with constant velocity in the same vertical plane at angles $30°$ and $60°$ with respect to the horizontal respectively as shown in the figure. The speed of $A$ is $100\sqrt{3}{ \mathrm{m} \mathrm{s}}^{-1}$. At time $t=0 \mathrm{s}\text{,}$ an observer in $A$ finds $B$ at a distance of $500 \mathrm{m}.$ This observer sees $B$ moving with a constant velocity perpendicular to the line of motion of $A.$ If at $t=t_0, A$ just escapes being hit by $B, t_0$ in seconds is

A ball is projected from the ground at an angle of $45°$ with the horizontal surface. It reaches a maximum height of $120 \mathrm{m}$ and returns to the ground. Upon hitting the ground for the first time, it loses half of its kinetic energy. Immediately after the bounce, the velocity of the ball makes an angle of $30°$ with the horizontal surface. The maximum height it reaches after the bounce, in metres, is...