Kinetic Energy And Projectile Motion

1. To determine the kinetic energy of a ball at the highest point of its flight, we begin by analyzing the components of motion:
   • A ball is projected at an angle of from the horizontal.
   • The kinetic energy of the ball at the point of projection can be associated with its initial velocity .
2. The kinetic energy at any point is given by the equation: .
3. At the highest point of the flight:
   • The ball's velocity is entirely horizontal, as the vertical component of velocity becomes zero.
   • The initial velocity can be decomposed into horizontal and vertical components:
     • Horizontal component: , which simplifies to .
     • Vertical component: .
4. At the highest point, the kinetic energy is due to the horizontal velocity only:
   • The horizontal velocity remains constant as .
5. The initial kinetic energy is:
6. Therefore, the kinetic energy of the ball at the highest point of its flight is .

The correct option is, therefore, .

Given:
Mass of ball,
Velocity,
Angle with horizontal =

Step 1: Initial Kinetic Energy

Step 2: Final Kinetic Energy

After the vertical component becomes zero, only the horizontal component remains.

Step 3: Decrease in Kinetic Energy

Substitute values:

Final Answer:

Decrease in kinetic energy = 15 J
✅ Correct Option: (2)