NASA launches a rocket

Question

NASA launches a rocket at 
t=0
seconds. Its height, in meters above sea-level, as a function of time is given by

h(t)=-4.9t2+175t+101

Assuming that the rocket will splash down into the ocean, at what time does splashdown occur?

The rocket splashes down after   seconds.

How high above sea-level does the rocket get at its peak?

The rocket peaks at   meters above sea-level.

Answer 1

h(t) = -4.9t² + 175t + 101

 

The rocket splashes down when h(t) = 0.  Set h(t) = 0 and solve the resulting quadratic equation for t.

 

-4.9t² + 175t + 101 = 0

 

t = 36.28 s  [Discard the negative solution, since time starts at t = 0.]

 

Peak height (h_max) occurs at the vertex of the h-t parabola, which is at

 

t = - 175/[2(-4.9)] s = 17.86 s

 

Peak height = h_max = h(17.86).

 

Just plug 17.86 s into h(t) and get the peak height.  You should be able to finish from here.