Question

A ball was thrown from height $H$ and the ball hits the floor with velocity $10(\hat{i}-\hat{j})\text{m/s},$ $1.5$ sec after its projection. Find initial speed of ball.

• A. $10\sqrt{5}\text{m/s}$
• B. $5\sqrt{5}\text{m/s}$
• C. $15\text{m/s}$
• D. $30\text{m/s}$

Answer 1

The correct option is B $5\sqrt{5}\text{m/s}$

Given that,
$1.5$ sec after projection,
$\overrightarrow{v_x}=10\hat{i}$
$\overrightarrow{v_y}=-10\hat{j}\overrightarrow{a}=-g\hat{j}=-10\hat{j}$
Now,
$\left(\overrightarrow{u_y}\right)=\overrightarrow{v_y}-\overrightarrow{a}t=-10\hat{j}-(-10\hat{j})\times \left(1.5\right)$
$\Rightarrow \overrightarrow{u_y}=5\hat{j}$
As there is no acceleration in horizontal direction,
$\overrightarrow{u_x}=\overrightarrow{v_x}=10\hat{i}$
Initial velocity vector,
$\overrightarrow{u}=\overrightarrow{u_x}+\overrightarrow{u_y}=10\hat{i}+5\hat{j}\Rightarrow |\overrightarrow{u}|=5\sqrt{5}\text{m/s}$