A 49.9-g golf ball is driven from the tee with an initial speed of 48.8 m/s and rises to a height of 24.0 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 5.42 m below its highest point?
a) KE=original KE-PE gained
= 1/2 m *48.8^2 - mg(24)
I am not sure I am understanding this answer. Also if you knew how to do part b
How can I do part B?
To find the kinetic energy of the ball at its highest point, we can use the principle of conservation of energy, which states that the total mechanical energy of a system remains constant when no external forces (like air resistance) are acting on it.
(a) To determine the kinetic energy at the highest point, we need to find the initial kinetic energy of the ball and the potential energy at its highest point.
The initial kinetic energy (K_initial) is given by the formula:
K_initial = (1/2) * m * v_initial^2
where m = mass of the ball = 49.9 g = 0.0499 kg
and v_initial = initial velocity of the ball = 48.8 m/s
Substituting the values, we have:
K_initial = (1/2) * 0.0499 kg * (48.8 m/s)^2
Simplifying the expression:
K_initial = 0.0499 kg * 1192.64 m^2/s^2
K_initial = 59.44 Joules
At the highest point, all the initial kinetic energy is converted into potential energy (PE). So, the potential energy (PE) is equal to the initial kinetic energy (K_initial).
PE = K_initial = 59.44 Joules
(b) To find the speed of the golf ball when it is 5.42 m below its highest point, we will use the principle of conservation of energy again.
Let's consider this point as the final point. At this point, the potential energy (PE_final) will be converted back into kinetic energy (K_final).
The potential energy (PE_final) at this point is given by:
PE_final = m * g * h
where m = mass of the ball = 49.9 g = 0.0499 kg
g = acceleration due to gravity = 9.8 m/s^2
h = height above the reference point (highest point) = 24.0 m - 5.42 m = 18.58 m
Substituting the values, we have:
PE_final = 0.0499 kg * 9.8 m/s^2 * 18.58 m
Simplifying the expression:
PE_final = 0.0499 kg * 9.8 m/s^2 * 18.58 m
PE_final = 8.99 Joules
The final kinetic energy (K_final) will be equal to the potential energy (PE_final) at this point.
K_final = PE_final = 8.99 Joules
To find the speed (v_final), we will use the kinetic energy formula:
K_final = (1/2) * m * v_final^2
Solving for v_final:
v_final^2 = (2 * K_final) / m
v_final = sqrt((2 * K_final) / m)
Substituting the values, we have:
v_final = sqrt((2 * 8.99 Joules) / 0.0499 kg)
v_final = sqrt(359.64 m^2/s^2 / 0.0499 kg)
v_final = sqrt(7208.417 m^2/s^2 / kg)
v_final = 26.86 m/s
Therefore, the speed of the golf ball when it is 5.42 m below its highest point is approximately 26.86 m/s.