BM Sharma Solutions for Chapter: Motion in Two Dimensions, Exercise 2: DPP

Three stones $A\text{,} B$ and $C$ are simultaneously projected from the same point with the same speed. $A$ is thrown upwards. $B$ is thrown horizontally and $C$ is thrown downwards from a building. When the distance between stones $A$ and $C$ becomes $10 \mathrm{m}$, then distance between $A$ and $B$ will be

A stone projected at an angle of $60°$ from the ground level strikes at an angle of $30°$ on the roof of a building of height $h$. The speed of projection of the stone is

A bullet, fired from the horizontal ground at some angle, passes through the point $P=\left(\frac{3R}{4},\frac{R}{4}\right)$, where $R$ is the range of the bullet. Assume that the point of the fire is at the origin and the bullet moves in $x-y$ plane with $x-\mathrm{axis}$ horizontal and $y-\mathrm{axis}$ vertically upwards. Then, the angle of projection is

An aircraft moving with a speed of $972 \mathrm{km} {\mathrm{h}}^{-1}$ is at a height of $6000 \mathrm{m}$, just overhead of an anti-aircraft gun. The muzzle velocity of the gun is $540 \mathrm{m} {\mathrm{s}}^{-1}$. Find the firing angle $\theta$ for which the bullet hit the aircraft.

A stone is projected from ground level such that its horizontal and vertical components of initial velocity are $u_x=10 \mathrm{m} {\mathrm{s}}^{-1}$ and $u_y=20 \mathrm{m} {\mathrm{s}}^{-1}$, respectively. The angle between the velocity vector of the stone, one second before and one second after it attains maximum height, is

In the climax of a movie, the hero jumps from a helicopter, and the villain, chasing the hero, also jumps from the same level. After some time, when they come at the same horizontal level, the villain fires a bullet horizontally towards the hero. Both were falling with a constant acceleration of $2 \mathrm{m} {\mathrm{s}}^{-2}$, because of a parachute. Assuming the hero to be within the range of the bullet, which of the following is correct?

A football is kicked with a speed of $22 \mathrm{m} {\mathrm{s}}^{-1}$ at an angle of $60°$ to the positive $x$ direction, taken along the horizontal. At that instant, an observer moves past the football in a car that moves with a constant speed of $11\mathrm{ }\mathrm{m} {\mathrm{s}}^{-1}$ in the positive $x$ direction. Take positive $y$direction vertically upwards.$(g=10 \mathrm{m} {\mathrm{s}}^{-2})$

A particle is projected from a horizontal floor with speed $10 \mathrm{m} {\mathrm{s}}^{-1}$ at an angle$30°$ with the floor, which strikes the floor after some time. Which of the following is correct?