SOLUTION: An object is projected upward with an initial velocity of 98ft/second. The rise and fall of the object is given by the equation s=98t-4.9t2, where s is the height above the ground

Question 1212: An object is projected upward with an initial velocity of 98ft/second. The rise and fall of the object is given by the equation s=98t-4.9t2, where s is the height above the ground and t is the time from the object's launch. Find the maximum height and the time this occurs?
Answer by khwang(438) (Show Source): You can put this solution on YOUR website!
s(t)=98t-4.9t^2,
s'(t) = 98 - 9.8 t,
Solve s'(t) = 0, i.e. 98 - 9.8 t = 0, or 9.8 t = 98,
we have t = 10 sec.
Since s"(t) = -9.8 < 0 for all t, by the 2nd derivative test,
s has maximum value when t = 10 sec.
We see that the maximum height is s(10) = 980 - 4.9 *100 = 490 meters.
If you don't know derivative.
Use s(t)=98t-4.9t^2 = -4.9(t^2 - 20t + 100) + 490
= -4.9(t - 10)^2 + 490 (<= 490)
We can see that s(t) has max value 490 when t = 10.
Or use the formula v(velocity) = 98 - 9.8 t.
If v =0, the height is max.
Solve v = 98 - 9.8 t = 0, we get t = 10 sec

RELATED QUESTIONS
An object is projected vertically upward with an initial velocity of Vo ft/sec, and its... (answered by stanbon)

In physics, one learns that the height of an object thrown upward from an initial height... (answered by Boreal)

hi please i need your help with this problem an object is projected vertically... (answered by jorel1380)

The height of an object thrown upward from the floor of a canyon 106 feet deep with an... (answered by stanbon)

If an object is thrown upward with an initial velocity of 96ft. per second, its height... (answered by Alan3354)

If an object is projected upward with an initial velocity of 48 ft pe second from a... (answered by ankor@dixie-net.com,Earlsdon)

Please help me solve this problem: If an object is projected upward with an initial... (answered by richwmiller)

Please help me solve this: If an object is projected upward with an initial velocity of... (answered by Alan3354)

If an object on Earth is projected upward with an initial velocity of 32 feet per second, (answered by jim_thompson5910)