Final answer:
To calculate the maximum height that a tennis ball will reach when served with an initial velocity of 120 feet per second from a height of 2 feet, we use the kinematic equations for projectile motion. By considering the acceleration due to gravity and the initial speed, the maximum height is found to be 227 feet.
Step-by-step explanation:
Calculating Maximum Height of the Ball
The question asks us to determine the maximum height a tennis ball reaches when served vertically with an initial speed. To solve this problem, we use the kinematic equations for projectile motion under gravity. The relevant equation here is:
v2 = u2 + 2gh,
where:
- v is the final velocity (0 m/s at maximum height),
- u is the initial velocity (120 ft/s),
- g is the acceleration due to gravity (-32 ft/s2), and
- h is the height.
Rearranging the equation to solve for h, we get:
h = (v2 - u2) / (2g)
By plugging the values into the equation:
h = (0 - (120)-2) / (2 * -32) = 225 ft
The total maximum height is the sum of the initial height and the height achieved from the serve:
Total Maximum Height = Initial Height + Height from Serve = 2 ft + 225 ft = 227 feet.
This is the maximum height the tennis ball will attain.