Q: A projectile of 2 kg has velocities 3 m/s and 4 m/s at two points during its flight in the uniform gravitational field of the earth. If these two velocities are perpendicular to each other then the minimum KE of the particle during its flight is

Sol. v_{1} cosα = v_{2} cos(90-α)

3 cos α = 4 sin α

$\large tan\alpha = \frac{3}{4} $

$\large K.E_{min} = \frac{1}{2}m v_1^2 cos^2\alpha$

$\large = \frac{1}{2}\times 2 \times 3^2 (\frac{4}{5})^2 $

= 5.76 J