Answer:
9090 m, 104 s
Explanation:
After the acceleration phase, the rocket reaches a height of:
x = x₀ + v₀ t + ½ at²
x = (0 m) + (0 m/s) (30 s) + ½ (10 m/s²) (30 s)²
x = 4500 m
And it reaches a velocity of:
v = at + v₀
v = (10 m/s²) (30 s) + (0 m/s)
v = 300 m/s
After the fuel runs out, the rocket goes into free fall. The maximum height reached is:
v² = v₀² + 2a(x - x₀)
(0 m/s)² = (300 m/s)² + 2(-9.8 m/s²)(x - 4500 m)
x ≈ 9090 m
The time to reach maximum height during free fall:
v = at + v₀
0 m/s = (-9.8 m/s²) t + (300 m/s)
t ≈ 30.6 s
And the time to land from the maximum height:
x = x₀ + v₀ t + ½ at²
0 m = (9090 m) + (0 m/s) t + ½ (-9.8 m/s²) t²
t ≈ 43.1 s
So the total time is:
t = 30 s + 30.6 s + 43.1 s
t ≈ 104 seconds
