Embibe Experts Solutions for Exercise 8: Assignment

Which of the following statements is/are correct?

A particle is projected with speed $10\sqrt{2} \mathrm{m} {\mathrm{s}}^{-1}$ from top of a tower of height $H$ as shown in figure
(take $H=10 \mathrm{m}$and $g=10 \mathrm{m} {\mathrm{s}}^{-2}$ ). Then

A swimmer at a point $A$ on the river bank wants to cross it. River is flowing with speed $v_0.$ (Refer the diagram below). If $v_{sr}$ denotes velocity of swimmer in still water, then

A particle starts performing circular motion in a circle of radius $1 \mathrm{m}$ at $t=0.$ Its speed $v$ varies with time $t$  as, $v=4t \mathrm{m} {\mathrm{s}}^{-1}.$ where $t$ is in seconds. If $a_r$ and $a_t$ are the radial and tangential acceleration of the particle respectively, then

Two particles $A$ and $B$ are at rest at separation of $160 \mathrm{m}.$ Both the particle starts moving at $t=$ $0.$ Particle A moves in a straight line perpendicular to initial position $AB$ with constant acceleration of $3 \mathrm{m} {\mathrm{s}}^{-2}.$ Particle $B$ moves in such a way that it always aims towards $A$ and moves with speed increasing at constant rate of $5 \mathrm{m} {\mathrm{s}}^{-2}.$ Then

A particle is projected from ground to ground and its path is as shown in the figure. Points $A$ and $B$ are at same horizontal level and points $C$ and $D$ are at another same horizontal level. Separation between line $AB$ and $CD$ is $5 \mathrm{m}.$ If particle takes time $t_1$ to go from $A$ to $B$ and time $t_2$ from $C$ to $D,$ then is $\left(g=10 \mathrm{m} {\mathrm{s}}^{-2}\right)$

A stone is projected horizontally with velocity $v$  from a building of height $h.$ It hits the inclined plane perpendicularly as shown in figure. Then

Two projectiles are projected from same position under gravity at different angles with horizontal in the same vertical plane. If velocity of one with respect to other is $v,$ acceleration of one with respect to other is $a$ and position of one with respect to other is $r,$ then which of the following graphs is(are) correct?