A newly established colony on the Moon launches a capsule vertically with an initial speed of 1.453 km/s. Ignoring the rotation of the Moon, what is the maximum height reached by the cap
g on the moon is 1.62 m/s^2
v^2 = 2gh ... h = v^2 / (2 g)
1.453km/s = 1,453 m/s.
V^2 = Vo^2 + 2g*h.
0 = 1453^2 - 3.24h,
h = ?
To find the maximum height reached by the capsule, we need to consider its vertical motion. We can use the principles of projectile motion to calculate this.
First, we need to identify the initial velocity of the capsule in the vertical direction. Since the capsule is launched vertically, the initial velocity in the vertical direction is equal to the initial speed of 1.453 km/s.
Next, we need to determine the acceleration acting on the capsule. On the Moon, the acceleration due to gravity is approximately 1.622 m/s², which is about 1/6th of the acceleration due to gravity on Earth.
Using the equation of motion for vertical motion:
vf² = vi² + 2ad
Where:
- vf is the final velocity (which is 0 m/s at the maximum height),
- vi is the initial velocity,
- a is the acceleration, and
- d is the displacement.
Since the final velocity is 0 m/s at the maximum height, we can rearrange the equation:
d = (vf² - vi²) / (2a)
Substituting the values:
d = (0 - (1453 m/s)²) / (2 * (-1.622 m/s²))
By calculating this expression, we can find the maximum height reached by the capsule on the Moon.