A 51.9-g golf ball is driven from the tee with an initial speed of 50.8 m/s and rises to a height of 28.4 m. (a) Neglect air resistance and determine the kinetic energy of the ball at its highest point. (b) What is its speed when it is 6.08 m below its highest point?

To solve this problem, we need to use the principles of conservation of energy.

(a) First, let's find the initial kinetic energy (KE) of the golf ball when it is driven from the tee. The formula for kinetic energy is:

KE = (1/2) * mass * velocity^2

Given:
Mass of the golf ball (m) = 51.9 g = 0.0519 kg
Initial speed of the golf ball (v) = 50.8 m/s

Plugging these values into the formula, we get:

KE_initial = (1/2) * 0.0519 kg * (50.8 m/s)^2

Solving this equation will give us the initial kinetic energy of the golf ball.

(b) Now, let's find the speed of the golf ball when it is 6.08 m below its highest point. To do this, we need to consider the conservation of mechanical energy. At its highest point, the golf ball will have maximum potential energy and zero kinetic energy. As it descends, it loses potential energy but gains kinetic energy. We can equate the potential energy lost to the kinetic energy gained.

The potential energy (PE) of an object at height h is given by the formula:

PE = mass * gravity * height

Given:
Height below the highest point (h) = 6.08 m

We can calculate the potential energy at this height:

PE_at_h = 0.0519 kg * 9.8 m/s^2 * 6.08 m

Substituting the values into the formula, we can calculate the potential energy.

Next, we equate the potential energy lost to the kinetic energy gained:

PE_loss = KE_gain

Since the golf ball initially had zero potential energy but gained potential energy as it moved upwards, the potential energy lost is equal to the initial potential energy (which is zero).

Thus, we have:

0 = KE_gain

Finally, solving for the kinetic energy gained, we can use the formula for kinetic energy with the mass of the golf ball and the speed at the desired position. Substituting the known values, we can find the kinetic energy (and consequently, the speed) at 6.08 m below the highest point.