Question

A man is standing on a cart moving with a constant velocity $10\text{m/s}$, facing the direction of motion, throws a ball vertically upwards at $5\text{m/s}$ with respect to himself. Then as observed from ground the ball will follow

• A. a straight line path
• B. a parabolic path
• C. a circular path
• D. Data insufficient

Answer 1

The correct option is B a parabolic path

Let us take $+vex$ direction along the direction of motion of car.
velocity of cart w.r.t ground is $\overrightarrow{v_{C,G}}=10\text{m/s}\hat{i}$
$\Rightarrow$velocity of ball with respect to cart is,
$\overrightarrow{v_{B,C}}=5\text{m/s}\hat{j}$
Hence, velocity of ball with respect to ground $\left(\overrightarrow{v_{B,G}}\right)$ is,
$\overrightarrow{v_{B,G}}=\overrightarrow{v_{B,C}}+\overrightarrow{v_{C,G}}$
$\Rightarrow \overrightarrow{v_{B,G}}=5\text{m/s}\hat{j}+10\text{m/s}\hat{i}$
$\overrightarrow{a_{B,G}}=-g\hat{j}=-10{\text{m/s}}^2\hat{j}$

$\because$ projected ball has velocity component in $x\&y$ directions w.r.t ground, and its acceleration is $g$ downwards.
$\therefore$ Ball will follow parabolic path (projectile motion) as observed from ground.
$\Rightarrow v=\sqrt{5^2+{10}^2}=5\sqrt{5}\text{m/s}$ is the speed of projection, and $R$ is the range of ball.