Word problem algebra

Question

An arrow is launched upward with a velocity of 192 feet per second from the top of a 35 foot building. What is the maximum height attained by the arrow?

Answer 1

h(t) = -16t^2 + `192t +35

h'(t) = -32t + 192 =0

t = 192/32 = 6 seconds to reach max height

max height = h(6) = -16(6^2) + 192(6) + 35

= (6)(-96+ 192) +35

= 6(96) + 35

= 576 +35

= 611 feet

Answer 2

Raymond's answer is perfect!

However, if you have not taken calculus, you can still find the maximum height of a parabola (vertex) by finding the axis of symmetry using the equation x = -b/(2a)

Using the equation Raymond provided: h(t) = -16t^2 + 192t +35 we have a = -16, b = 192, and c = 35

x = -b/(2a)

x = -192/(2(-16))

x = -192/-32

x = 6

Then use x = 6 with your original equation to find the maximum height, as Raymond already described.