Word problem

Question

the length of time t a satellite takes to complete a circular orbit of earth varies directly as the radius of the orbit r and inversely as the orbital velocity v if satellite. write the equation of variation using k as the constant of variation. if t=1.59 hours when r=4350 miles and v=17,000 miles per hour find t to two decimal places for r=4700 miles and v=21500mph

Answer 1

I love satellites. I'm ex-NASA. :-)

 

The linear distance a satellite travels in orbit is vt = kr.

 

So the travel time is t = kr/v and for the units of this problem, k is unitless. Which assumes a constant velocity.

 

If r=4350 miles and v=17000 MPH at t=1.59 hr, then k = about 6.21.

 

So for r=4700 miles and v=21500 MPH, using the same k, you get

 

t = about 1.36 hr. Cheers!

Answer 2

Time varies directly with the radius means...  t = kr

Time varies inversely as the velocity means... t = k/v

 

Since time varies directly with the radius and inversely

with the velocity then ....   t = kr/v

Where k is the constant of variation

 

Plugging in the information given we need to find k

 

1.59 = 4350k/17000

From this solve for k

 

k = 17000(1.59)/4350 = 6.214

 

Now that we have k the equation is:

 

t = 6.214r/v

 

t = 6.214(4700)/21500

 

t = 1.36 hours