Question

How long does it take the baseball to reach its maximum

Answer 1

1.44 s

Explanation:

The expression that describes the height of the baseball at time t is:

`h(t) = -16t^2 +46 t +6`

where

6 ft is the initial heigth of the baseball at t = 0 s

+46 ft/s is the initial velocity of the baseball

`-32 ft/s^2` 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:

`v(t)=h'(t)=-16\cdot 2 t^(2-1) + 46 t^(1-1)+0 = -32t+46` (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:

`0=-32t+46\\32t=46\\t=(46)/(32)=1.44 s`