Question

A projectile is projected with an initial velocity $(4\hat{i}+5\hat{j})m/s$. Here $\hat{j}$ is the unit vector directed vertically upwards and unit vector $\hat{i}$ is in the horizontal direction. Velocity of the projectile (in m/s) just before it hits the ground is :

• A. $4\hat{i}-5\hat{j}$
• B. $-4\hat{i}-5\hat{j}$
• C. $4\hat{i}+5\hat{j}$
• D. $-4\hat{i}+5\hat{j}$

Answer 1

Answer: (A)

$4\hat{i}-5\hat{j}$

The projectile is moving under gravity in which vertically downward gravitational force acts on it. Therefore, horizontal velocity of the projectile remains same as $\left(4\hat{i}\right)m/s$. Trajectory of the projectile is a parabola which is symmetric as diagram given below shows. Therefore, velocity of the projectile in vertical direction when it hits the ground will be $(-5\hat{j})m/s$.
So, velocity of the projectile when it hits the ground, $v=4\hat{i}-5\hat{j}$.