Question

In 2004, the highest space plane flight was made by Brian Binnie in Space Sip One. A flight with this altitude can be modeled by the function h = -0.17t^2 + 187t + 61000, where h is the altitude in meters and t is flight time in seconds. What was the highest altitude reached by the space plane?​

Answer 1

Answer:

h = 11242 km

Step-by-step explanation:

A flight with this altitude can be modeled by the function :

$h = -0.17t^2 + 187t + 61000$ ....(1)

Where h is the altitude in meters and t is flight time in seconds.

We need to find the highest altitude reached by the space plane.

Put $\dfrac{dh}{dt}=0$

So,

$\dfrac{d(-0.17t^2 + 187t + 61000)}{dt}=0\\\\-0.34t+187=0\\\\0.34t=187\\\\t=\dfrac{187}{0.34}\\\\t=550\ s$

At t = 550 seconds the space plane reaches the highest altitude.

Put t = 550 s in equation (1).

$h = -0.17(550)^2 + 187(550)+ 61000\\\\h=112425\ m\\\\h=112.42\ km$

Hence, the highest altitude reaches by the space plane is 11242 km.