Embibe Experts Solutions for Exercise 3: Assignment

A train is running at a constant speed of $90 \mathrm{km} {\mathrm{h}}^{-1}$ on a straight track. A person standing at the top of a boggey moves in the direction of motion of the, train such that he covers $1$ meters on the train each second. The speed of the person with respect to ground is

A car with a vertical windshield moves in a rain storm at a speed of $40 \mathrm{km} {\mathrm{hr}}^{-1}$. The rain drops fall vertically with constant speed of $20 \mathrm{m} {\mathrm{s}}^{-1}$. The angle at which rain drops strike the windshield is

A body of mass $1 \mathrm{kg}$ is projected from ground at an angle $30°$ with horizontal on a level ground at a speed $50 \mathrm{m}\hspace{0.17em}{\mathrm{s}}^{-1}$. The magnitude of change in momentum of the body during its flight is $\left(g=10 \mathrm{m} {\mathrm{s}}^{-2}\right)$

Two projectiles are projected at angles $\left(\frac{\pi }{4}+\theta \right)$ and $\left(\frac{\pi }{4}-\theta \right)$ with the horizontal, where $\theta <\frac{\pi }{4}$, with same speed. The ratio of horizontal ranges described by them is

The position coordinates of a projectile projected from ground on a certain planet (with no atmosphere) are given by $y=\left(4t-2t^2\right)\mathrm{m}$ and $x=(3 t)$ metre, where $t$ is in second and point of projection is taken as origin. The angle of projection of projectile with vertical is

A particle is projected from ground with speed $80 \mathrm{m}\hspace{0.17em}{\mathrm{s}}^{-1}$ at an angle $30°$ with horizontal from ground. The magnitude of average velocity of particle in time interval $t=2 \mathrm{s}$ to $t=6 \mathrm{s}$ is [Take $g=10 \mathrm{m}\hspace{0.17em}{\mathrm{s}}^{-2}$]

A stone projected from ground with certain speed at an angle $\theta$ with horizontal attains maximum height $h_1$. When it is projected with same speed at an angle $\theta$ with vertical attains height $h_2$. The horizontal range of projectile is

The angle of projection of a projectile which is projected with certain velocity from ground is $\frac{\pi }{8}$ with horizontal and its horizontal range is $R.$ The angle with the horizontal for another projectile having same range $R$ and speed is