Ashok Sharma Solutions for Chapter: Description of Motion in Two and Three Dimensions, Exercise 1: SELF EVALUATION TEST

Does the nature of vector change when it is multiplied by a scalar?

Can $\left|\overrightarrow{A}+\overrightarrow{B}\right|=\left|\overrightarrow{A}-\overrightarrow{B}\right|$ ?

When can the resultant vector be zero?

Show that the range of a projectile for two angles $\alpha$ and $\beta$ is the same where $\alpha +\beta ={90}^{\circ }$.

What is centripetal acceleration? Derive an expression for it in terms of constant speed of the body.

A stone thrown horizontally falls on the ground after $0.5 \mathrm{s}$ at a distance of $5 \mathrm{m}$from where it was thrown. ($a$) From what height was it thrown? ($b$) what was the initial velocity? ($c$) with what velocity did the stone touch the ground? ($d$) what angle was formed by the trajectory of the stone with the ground?

A projectile is fired with a velocity making an angle $\theta$ with the horizontal. Show that it follows a parabolic trajectory. Obtain an expression for the maximum height attained by it.

Define parallelogram law of vector addition. Calculate the magnitude and direction of the resultant vector of two vectors $P$ and $Q$ acting at angle $\theta$. What happen to the resultant vector if the given vectors are collinear or anti-collinear in nature?