A 47.8-g golf ball is driven from the tee with an initial speed of 53.6 m/s and rises to a height of 32.6 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 7.24 m below its highest point?
To solve this problem, we need to use the principles of conservation of energy.
(a) To determine the kinetic energy of the golf ball at its highest point, we need to find its potential energy at that point and subtract it from the initial total mechanical energy.
Step 1: Find the potential energy at the highest point:
Potential Energy = mass * gravity * height
Given:
Mass of the golf ball (m) = 47.8 g = 0.0478 kg
Height (h) = 32.6 m
Acceleration due to gravity (g) = 9.8 m/s^2
Potential Energy = 0.0478 kg * 9.8 m/s^2 * 32.6 m
Step 2: Find the initial kinetic energy:
Kinetic Energy = 0.5 * mass * velocity^2
Given:
Initial speed of the golf ball (v) = 53.6 m/s
Kinetic Energy = 0.5 * 0.0478 kg * (53.6 m/s)^2
Step 3: Determine the kinetic energy at the highest point:
Kinetic Energy at highest point = Initial Kinetic Energy - Potential Energy
(b) To find the speed of the golf ball when it is 7.24 m below its highest point, we will again use the principles of conservation of energy.
Step 1: Determine the potential energy at a height of 7.24 m below the highest point:
Potential Energy = mass * gravity * height
Given:
Height (h) = 7.24 m
Potential Energy = 0.0478 kg * 9.8 m/s^2 * 7.24 m
Step 2: Determine the kinetic energy at that point:
Kinetic Energy = Total Mechanical Energy - Potential Energy
To find the total mechanical energy, we can use the same value we found for the initial kinetic energy in part (a).
Kinetic Energy at 7.24 m below the highest point = Initial Kinetic Energy - Potential Energy
Finally, to find the speed at this point, we need to calculate the velocity using the equation:
Velocity = √(2 * Kinetic Energy / mass)
Keep in mind that these calculations neglect air resistance, so the answers may not be entirely accurate in real-world scenarios.