Answer:
It takes the ball 1.837 s to reach its maximum height.
Explanation:
Hi there!
First, let´s write the function h(t):
h(t) = -4.9 · t² + 18 · t + 7
The velocity of the ball is the variation of height over time, in other words, the velocity is the derivative of the function height with respect to time:
v = dh/dt = -2 · 4.9 · t + 18 = -9.8 · t + 18
When the ball reaches its maximum height, its velocity is zero. Then, at the maximum height dh/dt = 0. We can use this to obtain the time it takes the ball to reach the maximum height:
v = -9.8 · t + 18
0 = -9.8 · t + 18
-18 / -9.8 = t
t = 1.837 s
It takes the ball 1.837 s to reach its maximum height.
Have a nice day!
