Embibe Experts Solutions for Chapter: Kinematics, Exercise 3: Level 3

The angle between two vectors $x$ and $y$ is $\theta$. If the resultant vector $z$ makes an angle $\frac{\theta }{2}$ with $x$, then which of the following is true?

M.S. Dhoni hits two cricket balls in the air in a $T-20$ match. Both the balls leave his bat at the same velocity but at different angles of $30°$ and $60°$ respectively. If one ignores air friction and wind velocity, which of the following statements is correct? (Angles are with respect to the horizontal)

A ball is thrown horizontally from a height of $100 \mathrm{m}$ with an initial speed of $15 \mathrm{m}/\mathrm{s}$. How far does it travel horizontally in the first $2$ seconds?

The equation of motion of a body is, $\frac{\mathrm{d}v\left(t\right)}{\mathrm{d}t}=9-3v\left(t\right)$ where, $v\left(t\right)$ is the speed (in $\mathrm{m} {\mathrm{s}}^{-1}$) at time $t$ (in second). If the body was at rest at $t=0$, then which of the following is correct?

At$t=0 \mathrm{s},$  an object at origin has a velocity $\overrightarrow{v}=(2\hat{i}+4\hat{j}) \mathrm{m} {\mathrm{s}}^{-1}.$. If it is acted upon by an acceleration $a=(\hat{i}-3\hat{j}) \mathrm{m} {\mathrm{s}}^{-2}$ for a duration of $6$ seconds, find its coordinates at the end of $t=6$ seconds.

$\int \left(5-6x\right)dx$

The angular velocity of a ceiling fan reduces to $50\%$ after $36$ rotations since it is switched off. Assuming uniform retardation, the number of rotations it further makes before coming to rest is $\underline{ }$