Question

A body of mass $5~\text{kg}$ starts from the origin with an initial velocity $\vec{v}_0 = (30\hat{i} + 40\hat{j})~\text{m/s}$.
If a constant force $\vec{F} = -(i + 5j)~\text{N}$ acts on the body, then the time in which the y-component of its velocity becomes zero is

• A. $5~\text{s}$
• B. $20~\text{s}$
• C. $40~\text{s}$
• D. $80~\text{s}$

Hint:

To find time for velocity to become zero in a direction, use $v = u + at$ on that component.

Answer 1

The Correct Option is C

Mass $m = 5~\text{kg}$
Force in y-direction: $F_y = -5~\text{N}$
Acceleration in y-direction: $a_y = \dfrac{F_y}{m} = \dfrac{-5}{5} = -1~\text{m/s}^2$
Initial velocity in y-direction: $v_{y0} = 40~\text{m/s}$
Using the equation: $v = u + at$
$0 = 40 - 1 \cdot t \Rightarrow t = 40~\text{s}$