Embibe Experts Solutions for Chapter: Projectile Motion, Exercise 1: Exercise 1

Stone is projected from level ground. At a height $0.4 \mathrm{m}$ from the ground, the velocity of the stone in vector form is $\overrightarrow{u}=(6\hat{\mathrm{i}}+2\hat{\mathrm{j}}) \mathrm{m} {\mathrm{s}}^{-1}$ (the $\mathrm{x}$-axis is horizontal and $\mathrm{y}$-axis is vertically upwards). The angle of projection with horizontal is $\left(g=10 \mathrm{m} {\mathrm{s}}^{-2}\right)$

Neglect air resistance in this problem. A cannon simultaneously fires two identical cannonballs at targets $1$ and $2$ as shown below. If the cannonballs have identical initial speeds, which of the following statements is true? Assume the point of projection and targets to be at the same horizontal level.

From an elevated point $A$, stone is projected vertically upwards. When the stone reaches a distance $h$ below $A$ its velocity is double what it was at a height $h$ above $A$. The greatest height attained by the stone above $A$ is

A particle-$1$ is projected with speed $v_1$ from a point A making an angle of $30°$ with the vertical. At the same instant, a second particle- $2$ is thrown vertically upwards from point $B$. Both the particles reach height $H$, simultaneously. The ratio of $\frac{v_1}{v_2}$ is :

Two persons $X$ and $Y$ are playing with two different balls of masses $m$ and $2m$. If $X$ throws his ball vertically up and $Y$ at an angle $\theta$ with vertical, both of them stay in the air for the same time. The maximum heights attained by the two are in the ratio:

A gun is pointed towards a $100 \mathrm{m}$ high target as shown in the figure. Target is released at the same time when the gun is shot. To hit the target in the air, muzzle speed should not less than $\left(g=9.8 \mathrm{m} {\mathrm{s}}^{-2}\right)$

A fruit is falling with zero initial velocity from a $50 \mathrm{m}$ high tree. A man, who is at $50 \mathrm{m}$ horizontal distance from the tree fires a bullet with a speed of $10\sqrt{2} \mathrm{m} {\mathrm{s}}^{-1}$, at an angle $45°$ with horizontal. After how much time will the bullet hit the fruit?

A helicopter is flying at an altitude of $200 \mathrm{m}$ with $25 \mathrm{m} {\mathrm{s}}^{-1}$ at  an angle of $37°$ above horizontal when a package is dropped from it. After how much time (in sec) package hits the ground? $\left( \mathrm{g}=10 \mathrm{m} {\mathrm{s}}^{-2}\right)$