Embibe Experts Solutions for Chapter: Kinematics, Exercise 1: Exercise 1

In a circus, a performer throws an apple towards a hoop held at $45 \mathrm{m}$ height by another performer standing on a high platform (see figure below). The thrower aims for the hoop and throws the apple with a speed of $24 \mathrm{m} {\mathrm{s}}^{-1}$. At the exact moment that the thrower released the apple, the other performer drops the hoop. The hoop falls straight down. At what height above the ground does the apple go through the hoop?

A mobile phone of mass $100 \mathrm{g}$ falls from the hand of a person through the window of a train. The train is accelerating at $1 \mathrm{m} {\mathrm{s}}^{-2}$ and just $20 \mathrm{s}$ have passed since it left the station from standstill. If the window is $2 \mathrm{m}$ above the ground. With what kinetic energy will the phone will hit the ground? $\left(g=10 \mathrm{m} {\mathrm{s}}^{-2}\right)$

A thin metallic disc is rotating with constant angular velocity about a vertical axis that is perpendicular to its plane and passes through its centre. The rotation causes the free electrons in the disc to redistribute. Assume that, there is no external electric or magnetic field. Then,

A boat which has a speed of $5 \mathrm{km} {\mathrm{h}}^{-1}$ in still water crosses a river of width $1 \mathrm{km}$ along the shortest possible path in $15$ minutes. The velocity of the river water in $\mathrm{km} {\mathrm{h}}^{-1}$  is

Object $A$ moves uniformly with a constant speed $v$ to reach object $B$, while $B$ in turn moves rectilinearly with a uniform velocity of $u<\mathrm{v}$. At the initial moment $v$ is perpendicular to $u$ and the positions are separated by a distance $l$. The object $A$ meets the object $B$ at time $t$. The value of $t$  is

If $\overrightarrow{P}\times \overrightarrow{Q}=\overrightarrow{Q}\times \overrightarrow{P},$ the angle between $\overrightarrow{P}$ and $\overrightarrow{\mathrm{Q}}$ is $\mathrm{\theta } \left(0°<\mathrm{\theta }<360°\right).$ The value of $\mathrm{\theta }$ will be ________$°$.

Two trains, which are moving along different tracks in opposite directions towards each other, are put on the same track due to a mistake. Their drivers, on noticing the mistake, start slowing down the trains when the trains are $300 \mathrm{m}$ apart. Graphs given below show their velocities as a function of time as the trains slow down. What is the separation between the trains (in metre) when both have stopped?

  

A homogeneous disc with a radius $0.2 \mathrm{m}$ and mass $5 \mathrm{kg}$ rotates about an axis passing through its centre and perpendicular to its plane. The angular velocity of the rotating disc as a function of time is given by the formula $\omega =2+6\mathrm{t},$ where $\omega$ is in $\mathrm{rad} {\sec }^{-1}$ The tangential force applied to the rim of the disc is $x \mathrm{N}$. The value of $x$ is