Exercise - 1

A projectile is fired horizontally with a velocity of $98 \mathrm{m} {\mathrm{s}}^{-1}$ from the top of a hill $490 \mathrm{m}$ high.

$\left(1\right)$ Find the time is taken to reach the ground.

$\left(2\right)$ The distance of the target from the foot of the hill.

$\left(3\right)$The velocity with which the particle hits the ground.

A ball is thrown upwards and it returns to ground describing a parabolic path. Which of the following remains constant?

Three particles$P, Q$ and $R$ are placed as per the given figure. Masses of $P\mathit{,}\mathit{ }Q$ and $R$ are $\sqrt{3 m}, \sqrt{3 m}$ and $m$ respectively. The gravitational force on a fourth particle $S$ of mass $m$ is equal to

The velocity of end $A$ of rigid rod placed between two smooth vertical walls is $u$ along vertical direction. Find out the velocity of end $B$ of that rod, when it slips down.Rod always remains in contact with the vertical wall and also find the velocity of centre of mass of the rod. Also find equation of path of centre of rod.

A $3.0 \mathrm{kg}$ mass is moving in a plane with its $x$ and $y$ coordinates given by $x=5t^2–1$ and $y=3t^3+2$, where $x$ and $y$ are in meters and $t$ is in second. Find the magnitude of the net force acting on this mass at $t=2 \sec$.

There is an inclined surface of inclination $\mathrm{\theta }=30º$. A smooth groove is cut into it forming angle $\alpha$ with $AB$. A steel ball is free to slide along the groove. If the ball is released from the point $O$ at top end of the groove, the speed when it comes to $A$ is $[g=10 {\mathrm{ms}}^{-2}]$

A cuboidal car of height $3 \mathrm{m}$ is slipping on a smooth inclined plane. A bolt released from the roof of car from centre of roof $\left(P\right)$ then distance from centre of roof where bolt hits the floor with respect to car is

The figure shows at time $t=0 \mathrm{s}$, a rectangular and triangular pulse on a uniform wire are approaching each other. The pulse speed is $0.5 \mathrm{cm} {\mathrm{s}}^{-1}$. The resultant pulse at $t=2 \mathrm{second}$ is