A ball is thrown into the air with an upward velocity of 28 ft/s. Its height (h) in feet after t seconds is given by the function h = –16t² + 28t + 7. How long does it take the ball to reach its maximum height? What is the ball’s maximum height? Round to the nearest hundredth, if necessary.

A.1.75 s; 7 ft
B.0.88 s; 43.75 ft
C.0.88 s; 17.5 ft
D.0.88 s; 19.25 ft
I think it is D....?

h = -16t^2 + 28t + 7

dh/dt= -32t + 28 = 0 for a max of h
32t = 28
t = 28/32 = .875
when t = .875
h = -16(.875)^2 + 28(.875) + 7
= 19.25 ft


looks like D, you are correct

Its D guys don't worry

To find the time it takes for the ball to reach its maximum height, we need to determine the time when the ball's velocity becomes zero. The maximum height occurs when the velocity of the ball is zero because at that point, the ball starts descending.

The velocity equation is obtained by taking the derivative of the height equation with respect to time. In this case, the derivative of h(t) = -16t^2 + 28t + 7 is v(t) = -32t + 28.

Set the velocity equation equal to zero and solve for t:
-32t + 28 = 0
-32t = -28
t = -28/-32
t = 0.875 or approximately 0.88 seconds.

Therefore, the ball takes approximately 0.88 seconds to reach its maximum height.

To find the maximum height of the ball, substitute the time value obtained (0.88 seconds) into the height equation:
h(0.88) = -16(0.88)^2 + 28(0.88) + 7
h(0.88) = -12.544 + 24.64 + 7
h(0.88) = 19.096 or approximately 19.1 feet.

Therefore, the ball reaches a maximum height of approximately 19.1 feet.

So, the correct answer is D. 0.88 s; 19.25 ft

To find the time it takes for the ball to reach its maximum height, we need to determine the vertex of the quadratic equation. The vertex of a quadratic equation in the form of y = ax² + bx + c is given by the formula x = -b / (2a).

For the given equation h = -16t² + 28t + 7, we can see that a = -16 and b = 28. Substituting these values into the equation x = -b / (2a), we get:

t = -28 / (2 * -16)
t = -28 / -32
t = 0.875

Rounded to the nearest hundredth, the time it takes for the ball to reach its maximum height is approximately 0.88 seconds. Therefore, option B and option C are possible answers.

Next, we need to determine the maximum height of the ball. To find the maximum height, substitute the value of t we just found (0.88 seconds) into the given equation:

h = -16(0.88)² + 28(0.88) + 7
h = -16(0.7744) + 24.64 + 7
h = -12.3904 + 24.64 + 7
h = 19.2496

Rounded to the nearest hundredth, the maximum height of the ball is approximately 19.25 feet. Therefore, the correct answer is option D - 0.88 seconds; 19.25 feet.