A 50.3-g golf ball is driven from the tee with an initial speed of 57.0 m/s and rises to a height of 33.2 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 7.04 m below its highest point?
KE=initial KE-mgh
How do I figure out the speed then?
ke final=1/2 m vf^2
initial KE= 1/2 m vi^2
To answer part (a), we need to find the kinetic energy of the golf ball at its highest point.
The kinetic energy of an object is given by the formula: KE = (1/2)mv^2, where KE is the kinetic energy, m is the mass of the object, and v is the velocity of the object.
In this case, we are given the mass of the golf ball, which is 50.3 grams. However, the formula requires the mass to be in kilograms, so we need to convert the mass to kilograms by dividing it by 1000:
m = 50.3 g / 1000 = 0.0503 kg
We are also given the initial speed of the golf ball, which is 57.0 m/s. Since the golf ball is at its highest point, it has come to a stop momentarily, so its velocity is 0 m/s.
Plugging the values into the formula, we can calculate the kinetic energy:
KE = (1/2) * 0.0503 kg * (57.0 m/s)^2
= 81.03615 Joules
Therefore, the kinetic energy of the golf ball at its highest point is approximately 81.036 Joules.
To answer part (b), we need to find the speed of the golf ball when it is 7.04 m below its highest point.
To do this, we can use the principle of conservation of energy. At its highest point, the golf ball only has gravitational potential energy. As it falls, this potential energy is converted into kinetic energy. So, we can equate the initial potential energy at the highest point to the kinetic energy when it is 7.04 m below.
Using the formula for gravitational potential energy: PE = mgh, where PE is the potential energy, m is the mass, g is the acceleration due to gravity (approximately 9.8 m/s^2), and h is the height.
Since the golf ball is now below its highest point, we need to subtract the distance it has fallen (7.04 m) from the initial height (33.2 m). So, the height h is:
h = 33.2 m - 7.04 m = 26.16 m
The potential energy at the highest point, PE, is given by:
PE = mgh = 0.0503 kg * 9.8 m/s^2 * 33.2 m = 16.018428 Joules
The kinetic energy when it is 7.04 m below its highest point is equal to the potential energy at the highest point. So, we have:
KE = PE = 16.018428 Joules
To find the velocity (speed), we can rearrange the kinetic energy formula: KE = (1/2)mv^2 and solve for v:
v^2 = (2 * KE) / m
v^2 = (2 * 16.018428 Joules) / 0.0503 kg
v^2 = 634.943694 Joules / kg
Taking the square root of both sides, we find:
v = sqrt(634.943694 Joules / kg)
≈ 25.20 m/s
Therefore, the speed of the golf ball when it is 7.04 m below its highest point is approximately 25.20 m/s.