Question

A shuttle is being launched off a planet that has no air. The planet has a radius of 4.18×10⁶ m and a mass of 3.04×10²⁴ kg. The shuttle is fired off the planet at a speed of 5.20×10³ m/s. A small satellite is orbiting 750. m above the planet. What is the speed of the shuttle as it passes the satellite?

Answer 1

first we have to find the acceleration due to gravity in that planet which is expressed as,

g = G*M/R²

where G is gravitational constant,M is the mass of planet and R is its radius.

g = 6.67 * 10^-11 * 3.04 * 10^24/(4.18 * 10^6)^2

solving for g,

g = 11.6 m/s²

Now using third equation of motion,

V² - U² = 2*g*S

where V is the velocity when shuttle passes the satellite.g is the acceleration due to gravity and S is the distance covered which is given as 750 m. which is almost negligible but we will solve it for 750 m. In case you have mistakenly write so you can change the value of S in the expression.

putting all the values into above expression

V² = (5.20*10^3)² + 2*(-11.6)*750

V² = 27.04*10^6 - 17400

V = 5.198 * 10^3 m/s.

Thus the speed of shuttle when it passes satellite is 5.198 * 10^3 m/s