NCERT Solutions for Chapter: Motion in a Plane, Exercise 4: SA

A boy throws a ball in the air at $60°$to the horizontal along a road with a speed of $10 \mathrm{m} {\mathrm{s}}^{-1 }(36 \mathrm{km} {\mathrm{h}}^{-1})$. Another boy sitting in a passing by car observes the ball. Sketch the motion of the ball as observed by the boy in the car, if the car has a speed of $18 \mathrm{km} {\mathrm{h}}^{-1}$. Give an explanation to support your diagram.

In dealing with the motion of a projectile in the air, we ignore the effect of air resistance on the motion. This gives trajectory as a parabola as you have studied. What would the trajectory look like if air resistance is included? sketch such a trajectory and explain why you have drawn it that way.

A fighter plane is flying horizontally at an altitude of $1.5 \mathrm{km}$ with speed $720 \mathrm{km} {\mathrm{h}}^{-1}$. At What angle of sight (w.r.t horizontal) when the target is seen, should the pilot drop the bomb in order to attack the target?

Earth can be thought of as a sphere of radius $6400 \mathrm{km}$. Any object (or a person) is performing circular motion around the axis of the earth due to earth's rotation (period $1$ day). What is the acceleration of object on the surface of earth (at equator) towards its centre? What is it at latitude $\theta$ ? How does these accelerations compare with $\mathrm{g}=9.8 \mathrm{m} {\mathrm{s}}^{-2}$?

Earth also moves in circular orbit around sun once every year with an orbital radius of $1.5\times {10}^{11} \mathrm{m}$. What is the acceleration of earth (or any object on the surface of the earth) towards the centre of the sun? How does this acceleration compare with $\mathrm{g}=9·8 \mathrm{m} {\mathrm{s}}^{-2}$

Given below in column $\mathrm{{\rm I}}$ are the relations between vectors $a, b$ and $c$ and in column $\mathrm{{\rm I}{\rm I}}$ are the orientations of $a, b$ and $c$ in the $XY$ plane. Math the relation in column $\mathrm{{\rm I}}$ to correct orientations in column $\mathrm{{\rm I}{\rm I}}$. 

column I	column II
(a) $\overrightarrow{a}+\overrightarrow{b}=\overrightarrow{c}$	(i)
(b)$(\overrightarrow{a}-\overrightarrow{c})=\overrightarrow{b}$	(ii)
(c)$(\overrightarrow{b}-\overrightarrow{a})=\overrightarrow{c}$	(iii)
(d)$\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}=0$	(iv)

If $\left|A\right|=2$ and $\left|B\right|=4$ then match the relations in column I with the angle $\theta$ between $A$ and $B$ is column II.

If $\left|\overrightarrow{A}\right|=2$ and $\left|\overrightarrow{B}\right|=4,$ Then match the relations in column I with the angle $\theta$ between $A$ and $B$ in column II.