Question

Vanessa throws a tennis ball in the air. the function h(t) = -16t2 + 45t + 7 represents the distance, in feet, that the ball is from the ground at any time t. at what time, to the nearest tenth of a second, is the ball at its maximum height? t = seconds listen submit answer previous next

Answer 1

Given that height, h(t) of a tennis ball is modeled by the equation h(t)=-16t^2 + 45t + 7, the time taken for the ball to reach maximum height will found as follows:
at maximum height:
h'(t)=0
but from the equation:
h'(t)=-32t+45=0
solving for t we get
t=45/32
t=1.40625~1.4 seconds
Thus the time taken to reach maximum height is 1.4 seconds

Answer 2

The tennis ball reaches a maximum height at 1.4 seconds

The function of height of the tennis ball in air is given as:

$h(t) = -16t^2 + 45t + 7$

The time at which the tennis ball reaches a maximum height is calculated as:

$t = -\frac b{2a}$

Where:

a = -16, and b = 45

So, we have:

$t = -\frac {45}{2 *-16}$

Evaluate the quotient

$t = 1.4$

Hence, the tennis ball reaches a maximum height at 1.4 seconds

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