Question

Dump Tower is 96 stories tall. A small, 1.2-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 2.7 times the mass of Ganymede and the radius of the body is 1.7 times the radius of Makemake. You will track the object for its entire fall. Each story of this tower is 3.05 meters tall.
How many seconds will it take the object to reach the ground and what will be its impact speed with the ground?

Answer 1

Answer:

6.0 s

98 m/s

Explanation:

The radius of the planet is much bigger than the height of the tower, so we will assume the acceleration is constant.  Neglect air resistance.

Acceleration due to gravity on this planet is:

a = GM / r²

a = (6.67×10⁻¹¹ m³/kg/s²) (2.7 × 1.48×10²³ kg) / (1.7 × 750,000 m)²

a = 16.4 m/s²

The height of the tower is:

Δy = 96 × 3.05 m

Δy = 293 m

Given v₀ = 0 m/s, find t and v.

Δy = v₀ t + ½ at²

(293 m) = (0 m/s) t + ½ (16.4 m/s²) t²

t = 6.0 s

v² = v₀² + 2aΔy

v² = (0 m/s)² + 2 (16.4 m/s²) (293 m)

v = 98 m/s