I need help figuring out how to find maximum height, please.
A ball is thrown straight up from the top of a building 144 ft tall with an initial velocity of 164 ft per second. The distance [s(t)] in feet of the ball is given by s(t)=144+64t-162^2. Find the maximum height obtained by the ball.

Question

I need help figuring out how to find maximum height, please.
A ball is thrown straight up from the top of a building 144 ft tall with an initial velocity of 164 ft per second. The distance [s(t)] in feet of the ball is given by s(t)=144+64t-162^2. Find the maximum height obtained by the ball.

anonymous · Answer

I just don't even know where to begin, so any help is appreciated.

campbell_st · Answer

several methods for the solution

1. differentiate and solve for x... 


2. find the line of symmetry 

$$t = -\frac{b}{2a}$$

where b = 64 and t = -162

this will give the time when the ball is at the maximum height... 

substitute it into the original equation to find the max height.

anonymous · Answer

Can the t=-b/2a be used in every question like this?

campbell_st · Answer

if its a parabola... the max height is on the line of symmetry... 

if you know calculus you can differentiate and solve the 1st derivative.

anonymous · Answer

I honestly don't know calculus. What's the first step to solving this?

campbell_st · Answer

find the value of t

$$\frac{-64}{2 \times -162}$$

t = 0.19 secs


which seems small can you check your equation isn't - 16t^2

substitute t = 0.19 to find the maximum height