Question

A ball is thrown vertically upward. After t seconds, its height h (in feet) is given by the function n(t) = 461 - 161?. Afterhow long will it reach its maximum height? Round your answer to the nearest hundredth of a second.46 seconds1.44 seconds0.35 seconds2.88 seconds

Answer 1

Solution

Step 1

Write out the equation

$h(t)=46t-16t^2$

Step 2

Differentiate the equation to get the equation of the maximum height

$\frac{dh}{dt}=(1)46t^{1-1}-2(16)t^{2-1}$$\frac{dh}{dt}=\text{ 46-32t}$

Step 3

Equate the differentiated equation to zero and find the value of t at the maximum height

$\begin{gathered} 46-32t\text{ = 0} \\ 46\text{ = 32t} \\ \frac{46}{32}=\frac{32t}{32} \\ t\text{ = 1.44seconds} \end{gathered}$

To the nearest hundredth, the time t, it will take the ball to reach the maximum height when thrown vertically upwards is 1.44 seconds.

Hence the right answer is option B