The height h in feet of a ball t seconds after being tossed upwards is given by the function h(t) = 84 t - 16 t^2.
a. after how many seconds will it hit the ground?
b. what is its maximum height?

Question

The height h in feet of a ball t seconds after being tossed upwards is given by the function h(t) = 84 t - 16 t^2.
a. after how many seconds will it hit the ground?
b. what is its maximum height?

campbell_st · Answer

well let the height = 0 and solve

so you are looking at 

$$0 = 84t - 16t^2$$

the equation can be solved by factoring

campbell_st · Answer

the max height occurs when the time t is half way between the zeros for height, found in (a)

when you get the value of t, substitute it into the original equation to find the max height

anonymous · Answer

can you show me how? @campbell_st

campbell_st · Answer

well can you factor the quadratic...?

campbell_st · Answer

what if I suggested you take 4t out as a common factor, what would you have..?

anonymous · Answer

4t(21-4t) is that right? @campbell_st

campbell_st · Answer

yep thats its... so now what values of t make the equation equal zero. 

so you need to solve

4t = 0 

and 

21 - 4t = 0

what do you get

anonymous · Answer

t=0
t=-21/4 
 is that right?

campbell_st · Answer

thats almost correct... so the ball starts on the ground, t = 0 seconds, and then returns to the ground after t = 21/4 seconds

does that make sense... you had a slight error

 21 - 4t = 0..... so 21 = 4t ...etc

campbell_st · Answer

the curve is a parabola

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find the middle value, substitute it to find the max height. 

unless you have to use calculus