Question

A ball of mass 100 g is projected with velocity 20 m/s at $60^\circ$ with horizontal. The decrease in kinetic energy of the ball during the motion from point of projection to highest point is:

• A. 5 J
• B. 15 J
• C. 20 J
• D. zero

Hint:

In projectile motion, the loss in kinetic energy up to the highest point depends only on the vertical component of velocity.

Answer 1

The Correct Option is B

Concept:
In projectile motion:
The horizontal component of velocity remains constant.
The vertical component of velocity becomes zero at the highest point.
Decrease in kinetic energy from projection to highest point is equal to the loss of kinetic energy associated with the vertical component of velocity.
Step 1: Given data: \[ m = 100\,\text{g} = 0.1\,\text{kg}, \quad u = 20\,\text{m/s}, \quad \theta = 60^\circ \]
Step 2: Vertical component of velocity: \[ u_y = u \sin 60^\circ = 20 \times \frac{\sqrt{3}}{2} = 10\sqrt{3}\,\text{m/s} \]
Step 3: Kinetic energy associated with vertical motion: \[ \Delta K = \frac{1}{2} m u_y^2 \] \[ \Delta K = \frac{1}{2} \times 0.1 \times (10\sqrt{3})^2 \] \[ \Delta K = 0.05 \times 300 = 15\,\text{J} \]