Answer:
1.44 s
Step-by-step explanation:
The expression that describes the height of the baseball at time t is:
[tex]h(t) = -16t^2 +46 t +6[/tex]
where
6 ft is the initial heigth of the baseball at t = 0 s
+46 ft/s is the initial velocity of the baseball
[tex]-32 ft/s^2[/tex] is the acceleration of the baseball, downward
We can find an expression for the velocity of the baseball by calculating the derivative of the heigth; therefore we find:
[tex]v(t)=h'(t)=-16\cdot 2 t^{2-1} + 46 t^{1-1}+0 = -32t+46[/tex] (1)
The baseball reaches its maximum height when the vertical velocity becomes zero, so when
v(t) = 0
Substituting this into (1) and solving for t, we find the time at which this happens:
[tex]0=-32t+46\\32t=46\\t=\frac{46}{32}=1.44 s[/tex]
