Question

A satellite moves in a circular earth orbit that has a radius of 7.49 x 106 m. A model airplane is flying on a 24.1-m guideline in a horizontal circle. The guideline is nearly parallel to the ground. Find the speed of the plane such that the plane and the satellite have the same centripetal acceleration.

Answer 1

Step-by-step explanation:

Given

radius of satellite orbit
`r_1=7.49* 10^6 m`

And orbital velocity is given by

`v=\sqrt{(GM)/(r)}`

where M=mass of earth
`=5.98 * 10^(24) kg`

`G=6.67* 10^(-11)`

`v=\sqrt{(6.67* 10^(-11)* 5.98* 10^(24))/(7.49* 10^6)`

`v=7.29 * 10^3 m/s`

centripetal acceleration is given

`a_c=(v^2)/(r)`

`a_c=((7.29* 10^3)^2)/(7.49* 10^6)`

`a_c=7.095 m/s^2`

For Model airplane

`a_c=(v^2)/(r)`

`7.095=(v^2)/(24.1)`

`v=√(170.98)=13.07 m/s`