After \( t \) seconds, a ball tossed in the air from ground level reaches a height of \( h \) feet given by the equation:

\[ h = 144t - 16t^2 \]

Answer the following questions:

a. What is the height of the ball after 3 seconds?

b. What is the maximum height the ball will reach?

c. Find the number of seconds the ball is in the air when it reaches 224 feet in height.

d. After how many seconds will the ball hit the ground before rebounding?

Note: Consider whether to use the quadratic formula or another method to solve parts b, c, and d.

Don't modify the equation. It is true that f(3)= 288 for f(t) = -16t^2 +144t
the maximum height of the ball will be where the derivative is zero. In other words you could find the height of the ball by converting this into vertex form, or you could find it by calculating the time needed for the ball to reach its maximum height.
0=-32t+144
t=3 till max and max is 288
224=-16t^2 +144t 0= -16t^2+144t-224
t=2 but then the ball will reach 224 ft again at t=7
the ball reaches its maximum height at t=3 seconds and a parabola is symmetric, so at t=6 seconds it will contact the ground again.

Answered by mathdragon | 2024-06-10

After 3 seconds, the ball reaches a height of 288 feet. The maximum height of the ball is 324 feet, and it reaches 224 feet at approximately 2 seconds and again at 7 seconds. The ball will hit the ground after 9 seconds.
;

Answered by mathdragon | 2024-12-26