Question

The point from where a ball of mass $2\text{kg}$ is projected is taken as the origin of the co-ordinate axes. The $x$ and $y$ components of its displacement are given by $x=6t$ and $y=8t-5t^2$. Find the impulse ( in $\text{kg m/s}$) acting on it between the time $t=0$ to $t=2$ seconds

• A. $20$
• B. $40$
• C. $60$
• D. $80$

Answer 1

The correct option is B $40$

$u_x=6\text{m/s};u_y=8\text{m/s}$; and $g=10{\text{m/s}}^2$; In projectile motion, there is no change in velocity in the horizontal direction.
Hence there is no impulse in that direction. But in vertical direction, momentum changes. Hence $v_y-u_y=gt=20\text{m/s}$
Impulse $=m(v_y-u_y)=2\times 20=40\text{kg m/s}$.