Ritvik tosses a ball from where he stands on a balcony to his friend on the ground. The height, in feet, of the ball can be represented by the function d(t) = -16t² + 16t +9, where t represents time in seconds.

Question

Ritvik tosses a ball from where he stands on a balcony to his friend on the ground. The height, in feet, of the ball can be represented by the function d(t) = -16t² + 16t +9, where t represents time in seconds.

Part A: From what height was the ball tossed?
Part B: What is the maximum height of the ball?
Part C: How long does it take the ball to reach its maximum height?

Answer 1

Part A: To find the height from which the ball was tossed, we need to find d(0), which represents the initial height when t=0.

d(0) = -16(0)² + 16(0) + 9
d(0) = 9

Therefore, the ball was tossed from a height of 9 feet.

Part B: To find the maximum height of the ball, we need to determine the vertex of the parabolic function. The vertex can be found using the formula t = -b/2a.

In the function d(t) = -16t² + 16t +9,
a = -16, b = 16
t = -16/(2*-16) = 16/32 = 0.5

Now, substitute t=0.5 into the function to find the maximum height.

d(0.5) = -16(0.5)² + 16(0.5) + 9
d(0.5) = -4 + 8 + 9
d(0.5) = 13

Therefore, the maximum height of the ball is 13 feet.

Part C: To find how long it takes for the ball to reach its maximum height, we already found t=0.5, which is the time for the ball to reach its maximum height. Therefore, it takes 0.5 seconds for the ball to reach its maximum height.