In the above problem, the kinetic energy at the highest point for the second ball is K. What is the kinetic energy for the first balll

Correct Option: The correct answer is Zero.

Step-by-Step Explanation:

1. In projectile motion, when a body is projected at an angle with the horizontal, it possesses both horizontal and vertical components of velocity. At the highest point of its trajectory, the vertical component of velocity becomes zero, but the horizontal component of velocity remains active. Therefore, the body still has some non-zero velocity and consequently non-zero kinetic energy, which is given as $K$ for the second ball.

2. However, for a ball thrown vertically upwards (the first ball), the motion is purely vertical (at an angle of projection of 90 degrees to the horizontal). For such motion, there is no horizontal component of velocity.

3. At the highest point of vertical projection, the ball momentarily comes to a complete rest before starting its downward journey. Thus, its velocity at the highest point is:
$v=0$

4. The formula for kinetic energy is:
$E_k=\frac{1}{2}m{v}^2$

5. Substituting $v=0$ into the kinetic energy formula:
$E_k=\frac{1}{2}m(0{)}^2=0$

Therefore, the kinetic energy at the highest point for the first ball is zero.