A tennis ball machine serves a ball vertically into the air from a height of 2 feet, with an initial speed of 110 feet per second. After how many seconds does the ball attain its maximum height?
A) 2.87 sec
B) 3.44 sec
C) 4.65 sec
D) 5.41 sec
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Answer: B) 3.44 sec
Explanation:
It is launched vertically with an initial speed of 110 ft/sec.
It will reach maximum height when the speed drops to 0.
Vo=110 feet per second
ho=2 feet
So, h(t) = -16t^2 +110t +2
Take the derivative: h'(t) = 110 -32t
The maximum height will be at the inflection when the derivative crosses the x-axis, then h'(t)=0.
So, set h'(t)=0 and solve for t:
0 = 110 -32t
-110 = -32t
t=3.4375
t=3.44 seconds.
Explanation:
It is launched vertically with an initial speed of 110 ft/sec.
It will reach maximum height when the speed drops to 0.
Vo=110 feet per second
ho=2 feet
So, h(t) = -16t^2 +110t +2
Take the derivative: h'(t) = 110 -32t
The maximum height will be at the inflection when the derivative crosses the x-axis, then h'(t)=0.
So, set h'(t)=0 and solve for t:
0 = 110 -32t
-110 = -32t
t=3.4375
t=3.44 seconds.
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