Question

The height of a rocket, launched from the ground, is given by the function y = 30 t − 5 t 2 , where y is in meters and t is in seconds. An observer is sitting at ground level a distance d from the launch point. If r is the distance between the observer and where the rocket is, show that d r d t = ( 30 t − 5 t 2 ) ( 30 − 10 t ) √ ( 30 t − 5 t 2 ) 2 + d 2 . Show all your work.

Answer 1

1. (a) The orbital period can be calculated using the equation

T = 2πrr r

gR2

e

where r = Re + h

where re = 6378 km is the earth’s radius, r is the satellites distance

from the earth’s center and h = 205 km is the satellite’s orbital altitude, and g = 9.81m/s2

is the gravitational acceleration. With these

given values the orbital period is

Torbit = 5312.5s = 1.4757h