Question

The free-fall acceleration on a large asteroid, in the vacuum of space, is 0.45 m/s2. A spacecraft hovering 600 m above the surface drops a 25 kg payload wrapped in a padded jacket.

Answer 1

The approximate gravitational acceleration on the asteroid is 100m/s²

Step-by-step explanation:

The approximate gravitational acceleration on the asteroid can be calculated using the formula for free-fall motion. When the spacecraft is 100m closer to the surface of the asteroid, its velocity increases from 5m/s to 8m/s. We can use the following equation to find the acceleration:
Acceleration = (Final Velocity - Initial Velocity) / Time
Substituting the given values:
Acceleration = (8m/s - 5m/s) / 0.03s
Acceleration = 3m/s / 0.03s = 100m/s²
The approximate gravitational acceleration on the asteroid is 100m/s².

Answer 2

It will take approximately 8.88 seconds for the payload to reach the surface of the asteroid.

Step-by-step explanation:

The payload will fall to the surface of the asteroid at a constant acceleration of 0.45 m/s2 due to the gravitational force acting on it. The velocity of the payload at any time can be calculated using the following equation:

v = at

Where v is the velocity, a is the acceleration, and t is the time elapsed.

To find the time it takes for the payload to reach the surface, we can use the following equation:

d = vt + 0.5at^2

Where d is the distance traveled and t is the time elapsed.

We can rearrange this equation to solve for t:

t = (-v + sqrt(v^2 + 2ad)) / a

Plugging in the values given in the problem, we get:

t = (-0 + sqrt(0^2 + 2 * 0.45 * -600)) / 0.45

t = 8.88 seconds

Therefore, it will take approximately 8.88 seconds for the payload to reach the surface of the asteroid.