Answer:
The time taken by the object to reach the ground, t = 25.04 / √gₓ
The final velocity of the object, v = 23.39 √gₓ
Explanation:
Given data,
The height of the Dump Tower, h = 96 x 3.05
= 292.8 m
The mass of the planet housing Dump Tower, M = 2.7 mₓ
The radius of the planet housing Dump Tower, R = 1.7 rₐ
The acceleration due to the gravity of the planet is,
g = GM/R²
= 2.7 Gmₓ / (1.7 rₐ)²
= 0.934 Gmₓ/rₐ²
g = 0.934 gₓ
Using the II equations of motion,
S = ut + ½ gt²
= 0 + ½ (0.934 gₓ) t²
t = √(2S/ 0.934 gₓ)
= √(2 x 292.8/ 0.934 gₓ)
t = 25.04 / √gₓ
Hence, the time taken by the object to reach the ground, t = 25.04 / √gₓ
Using the I equations of motion
v = u + gt
= 0 + 0.934 gₓ (25.04 / √gₓ)
v = 23.39 √gₓ
Hence, the final velocity of the object, v = 23.39 √gₓ
