Question

Dump Tower is 77 stories tall. A small, 2.1-kg object is dropped over the side of the roof of the tower and accelerates toward the ground. The mass of the planet housing Dump Tower is unknown but the radius of the body is 0.5 times the radius of Titan. You will track the object for its entire fall. Each story of this tower is 2.86 meters tall.

What is the mass of the planet?

Fall time: 7.6s

Answer 1

radius of titan R = 2576 km = 2756*10^3 m

radius of planet r = 0.5*R = 0.5*2576*10^3 m = 1288000 m

gravitational force Fg = m*g

Fg = G*m*M/r^2

gravitaitonal acceleration g = GM/r^2

along vertical for free fall

initial velocity voy = 0

accelration ay = -g = -GM/r^2 = 6.67*10^-11*M/(1288000)^2

displacement y = -77*2.86 m

time of fall t = 7.6 s

y = voy*t + (1/2)*ay*t^2

-77*2.86 = -(1/2)*6.67*10^-11*M/(1288000)^2*7.6^2

mass of planet M = 1.89*10^23 Kg <<<------------ANSWER