Exercise (Conceptual Questions)

The coordinates of a particle moving in $xy$ plane vary with time as $\sqrt{x}=at; y=b{t}^2.$ The locus of the particle is:

Two paper screens A and B are separated by a distance of $100 m$. A bullet pierces A and then B. The hole in B is $10 cm$ below the hole in A. If the bullet is travelling horizontally at the time of hitting the screen A, calculate the velocity of the bullet when it hits the screen A. Neglect the resistance of paper and air.

A particle is projected horizontally with a speed of $\frac{20}{\sqrt{3}}{\mathrm{ms}}^{-1}$, from some height at $\mathrm{t}=0$.

what will be the displacement of the particle in $x$-direction when its velocity makes $60°$ angle with the initial velocity

A boy wants to jump from building $A$ to building $B$. Height of building $A$ is $25 \mathrm{m}$ and that of building $B$ is $5\mathrm{m}$. Distance between buildings is $4\mathrm{m}$. Assume that the boy jumps horizontally, then calculate minimum velocity with which he has to jump to land safely on building $\mathrm{B}$.

A tennis ball is dropped on the floor from a height of $20 \mathrm{m}$. It rebounds to a height of $5 \mathrm{m}$. The ball was in contact with third floor for $0.01 \mathrm{s}$. What was its average acceleration during the contact ? $(g=10 \mathrm{m} {\mathrm{s}}^{-2})$

A stone tied to the end of a string $1m$ long is whirled in a horizontal circle with constant speed. If the stone makes $22$ revolutions in $44 s$, what is the magnitude and direction of acceleration of the stone?

A body tied to astring of length L is revolved in a vertical circle with minimum velocity, when the body reaches the upper most point the string breaks and the body moves under the influence of the gravitational field of earth along a parabolic path. The horizontal range AC of the body will be :-
                

A mass tied to a string moves in a vertical circle with a uniform speed of $5 \mathrm{m} {\mathrm{s}}^{-1}$ as shown. At the point $P$ the string breaks. The mass will reach a height above P of nearly ($g=10 \mathrm{m} {\mathrm{s}}^{-2}$)