AP Calc word prob: For how many sec's is ball going up?

[venialove]

Use a(t) =-32 feet per second squared as the acceleration due to gravity. A ball is thrown vertically upward from the ground with an initial velocity of 56 feet per second. For how many seconds will the ball be going upward?

This is what I got so far
V=56f/s
Height=-32 ft
G=-9.81

I'm not sure what else I should do. There is no mass so I can't use mgh formula.

 

[Dr. Flim-Flam]

Re: math (ap cal word problem)

s(t) = -16t^2+vo(t)+so, vo = initial velocity, so = initial height, hence

s(t) = -16t^2 + 56t, s' (t) = v(t) = -32t + 56. When velocity = zero (max height) t = (7/4) sec.

 

[Deleted member 4993]

Re: math (ap cal word problem)

Use a(t) =-32 feet per second squared as the acceleration due to gravity. A ball is thrown vertically upward from the ground with an initial velocity of 56 feet per second. For how many seconds will the ball be going upward?

This is what I got so far
V=56f/s
Height=-32 ft
G=-9.81

I'm not sure what else I should do. There is no mass so I can't use mgh formula.

at the end of upward flight v = 0

Since it is calculus problem:

a = dv/dt

dv = a dt

v = at + C

v = 56 at t = 0

C = 56

v = at + 56

v = -32t + 56

At the end of upward flight, v = 0

t = 56/32 sec