Algebra 1 , Please Help!!

Question

Carly thinks that if she were able to dive from a 310 ft. position, she would experience a velocity that is twice as fast as if she were to dive from 155 ft.  Is She correct?  Explain why or why not.

Answer 1

h(t) = -16t^2 + ho = feet high

v(t) = -32t feet per second velocity

a(t) = -32 ft per second per second acceleration

h(t) = -16t^2 + 310 = 0

t^2 = 310/16

t= sqr310/4 = about 4.4 seconds

v(4.4) = -32(4.4) = -140.9 feet per second

h(t) = -16t^2 + 155 = 0

t^2 = 155/16 =

t= sqr155/4 = about 3.11 seconds

v(3.11) = -32(3.11) = - 99.6 feet per second

the velocity reached at ground level is less than twice as fast when starting at 310 as at 155

It's not twice as fast, it's the square of 2 as fast, about 1.414 times faster velocity.