SOLUTION: The path of a falling object is given by using the function s= -16t^2+ v sub0 t+ s sub0 where v sub0 represents the initial height in ft/sec and s sub0 represents the initial h

Question 150685: The path of a falling object is given by using the function s= -16t^2+ v sub0 t+ s sub0 where
v sub0 represents the initial height in ft/sec and
s sub0 represents the initial height in feet.
Also, s represents the height in feet of the object at any time, t which is measured in seconds.
A. If a rock is thrown upward with an initial velocity of 40 feet per second from the top of a 30 foot building, write the height (s) equation using this information...
I got.. -16t^2 + 40t + 30
B.How high is the rock after 2 seconds?
I got..
s(t)= -16(2)^2 + 40(2) + 30
s(t)= 46
C. After how many seconds will the graph reach maximum height? Show work algebraically.

D What is the maximum height?

I need help on C and D... and please tell me if I have figured A and B correctly... Thank you so very much.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Parts A and B are correct.

C)

From , we can see that , , and .

In order to find out when the rock will reach the max height, use this formula: .

Start with the given formula.

Plug in and .

Multiply 2 and to get .

Reduce.

So the rock will reach the max height when or . So the rock takes 1.25 seconds to reach the peak.

--------------------------
D)

Start with the given equation.

Plug in .

Square to get .

Multiply and to get .

Multiply and to get .

Combine like terms.

So at the peak, the rock is 55 feet high. So the max height is 55 feet.
RELATED QUESTIONS
The path of a falling object is given by the function S=-16t^2+v_o t+s_o where... (answered by ankor@dixie-net.com)

The path of a falling object is given by the function s+-16t^2+vot + so where... (answered by ankor@dixie-net.com)

1) The Path of a falling object is given by the function s=-16t^2+v^o t+s^o where v^o... (answered by jim_thompson5910)

The path of a falling object is given by the function s=-16t^+v*t+s If a rock is... (answered by jim_thompson5910)

The path of a falling object is given by the function s = -16t + vt + st where v... (answered by scott8148)

The path of a falling object is given by the function S=-16t^2+v_o t+s_o where v_o... (answered by Earlsdon)

the path of a falling object is given by the fuction s=-16t^2+v0t+s0 where v0 represents... (answered by scott8148)

a falling object is given by the function "S= -16t^2 + Vot + So" where "Vo" represents... (answered by stanbon)

I don't have alot but I always have trouble when it comes to word problems. Can you tell (answered by stanbon)