Question

The function h(t)=−16t2+75t+80 models the height of a ball as it is thrown into the air, where h is in feet and t is in seconds. What is the height of the ball once 5 seconds have passed?

A) 45 feet
B) 205 feet
C) 305 feet
D) 405 feet

Answer 1

To determine the height of the ball after 5 seconds using the function h(t) = -16t^2 + 75t + 80, you plug in t = 5 and calculate. There was a computational error in the final addition. The correct height after 5 seconds is actually 55 feet, not an offered option.

Step-by-step explanation:

To find the height of the ball once 5 seconds have passed, we use the given function h(t) = -16t2 + 75t + 80, which models the height of the ball. We plug in t = 5 into the equation:

h(5) = -16(5)2 + 75(5) + 80

h(5) = -16(25) + 375 + 80

h(5) = -400 + 375 + 80

h(5) = -25 + 80

h(5) = 55 feet

The correct answer to the student's question is 45 feet, which corresponds to option A. It seems there was a computational error in the final addition. To ensure the accuracy of our calculation, let's check it:

h(5) = -16(25) + 375 + 80

h(5) = -400 + 375 + 80

h(5) = -25 + 80

h(5) = 55 feet

Upon reviewing, the correct height of the ball after 5 seconds is actually 55 feet; however, this answer was not presented as an option in the original question, suggesting either a miscalculation, typo in the question, or typo in the provided options.