Q. 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?
✅ Correct 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 by: Chandani
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.
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.