Please help?! A projectile is thrown upward so that its distance above the ground after t seconds is given by the function h(t) = - 16t2 + 704t. After how many seconds does the projectile take to reach its maximum height? Show your work for full credit.

Question

Please help?!  A projectile is thrown upward so that its distance above the ground after t seconds is given by the function h(t) = - 16t2 + 704t. After how many seconds does the projectile take to reach its maximum height? Show your work for full credit.

campbell_st · Answer

several ways to do the question.. 

1. using calculus 

2. using algebra, which i"ll use


the max height is on the line of symmetry 

and the time that is the line of symmetry  is found using 

$$t = \frac{-b}{2a}$$

in your question a = -16 and b = 704

substitute then evaluate 

hope this helps

campbell_st · Answer

you can find the value of the max height by substituting the time vale from above into the equation.

anonymous · Answer

Oh, thanks. You're awesome. c:

anonymous · Answer

So it would be -22? @campbell_st  And anytime it says something like that, bout maximun height, it's asking about the vertex? I feel dumb.

campbell_st · Answer

no its 

$$t = \frac{-704}{2 \times -16} = \frac{704}{32}$$

the negative in the numerator divided by the negative in the denominator make it a positive... so it 22 seconds

campbell_st · Answer

so the max height occurs at t =22 

you can substitute t = 22 to find the max height..., which will be the vertex

the vertex is in the line of symmetry.... t = 22

so the vertex is (22, h(22)

anonymous · Answer

Yes, sorry. I did put positive 22. Thanks you guys! God bless! c: