Question

If a ball is thrown straight upwards with a velocity of 80 ft/s, then its height after t seconds is given by s = 80t - 16t2. Find the maximum height in feet reached by the ball.

Answer choices are:

72.35

80

150.25

100

Answer 1

s = 80t - 16t^2

One way to do it:

The ball starts at a height of 0 and ends at a height of 0.  Find when that happens.

0 = 80t - 16t^2

0 = t(80 - 16t)

80 - 16t = 0

80 = 16t

t = 5

The ball will return to the ground at t = 5 seconds.  The maximum height will happen halfway between the start at t = 0 and the end at t = 5.

Answer:  2.5 seconds.

.

Another way:

s = 80t - 16t^2 is an upside-down parabola.  The maximum height happens at the top of the parabola, where the parabola is flat (slope = 0, first derivative = 0).

s ' = 80 - 32t

0 = 80 - 32t

32t = 80

t = 2.5

Answer:  2.5 seconds.