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

Answer:

Explanation:

Given

radius of satellite orbit $r_1=7.49\times 10^6 m$

And orbital velocity is given by

$v=\sqrt{\frac{GM}{r}}$

where M=mass of earth $=5.98 \times 10^{24} kg$

$G=6.67\times 10^{-11}$

$v=\sqrt{\frac{6.67\times 10^{-11}\times 5.98\times 10^{24}}{7.49\times 10^6}$

$v=7.29 \times 10^3 m/s$

centripetal acceleration is given

$a_c=\frac{v^2}{r}$

$a_c=\frac{(7.29\times 10^3)^2}{7.49\times 10^6}$

$a_c=7.095 m/s^2$

For Model airplane

$a_c=\frac{v^2}{r}$

$7.095=\frac{v^2}{24.1}$

$v=\sqrt{170.98}=13.07 m/s$