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)=−4.9t^2+106t+157.

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)=−4.9t^2+106t+157.

A) How high above sea level is the rocket a the moment of launch?

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

C) At what time does the rocket reach its greatest height?

D) How high is the rocket at its greatest height?

Any help would be greatly appreciated. What formula to use when etc?

Answer 1

Sarah

(a) At the moment of launch t=0. So just find h (0)

(b) When it hits the sea, h(t)=0. So solve this. You can use the quadratic formula, or plot the function on a graphing calculator or Desmos and find the x intercept (I am using x instead of t here)

(c) h(t) is a quadratic, facing downwards. You need to find the t coordinate of the vertex. If h(t) = at² + bt + c, the t coordinate of the vertex will be t = -b/2a. You can also plot it, and read off the t coordinate of the vertex from your graph.

(d) You need to find h(t) at the vertex. So you can set t = -b/2a and find h(t), or find it from a graph.

Mike