Math homework help

Question

NASA launches a rocket at  seconds. Its height, in meters above sea-level, as a function of time is given by . Assuming that the rocket will splash down into the ocean, at what time does splashdown occur? A)The rocket splashes down after___ seconds. How high above sea-level does the rocket get at its peak? 

B)The rocket peaks at ___meters above sea-level.

Answer 1

Part A

This is a quadratic equation. We can set h(t) = to zero (sea level)

0 = -4.9t² +172t + 276

Solve for t using the quadratic formula (-b + or - the square root of (b² -4ac))/2a where a = -4.9, b = 172 and c = 276

So (-172 + SqRt(172² -(4)(-4.9)(276))/2(-4.9)

and (-172 - SqRt(172² -(4)(-4.9)(276))/2(-4.9)

-1.54 seconds and

36.64 seconds

Reject the negative answer so the rocket splashes down after 36.64 seconds

Part B

The x value of the vertex of a quadratic equation is -b/2a

so we have -172/2(-4.9) = 17.55 and is our t value in the equation

plug that t value into our equation to get the y value or the h(t) value in our equation

h(t) = -4.9(17.55)² +172(17.55) +176 = 1685.39 meters

This is our max height of the rocket