on the moon, where the local gravity has a magnitude of g=1.6 m/s^2, an astronaut jumps off the edge of a crater rim. It takes her 7.2 seconds to free fall to the crater floor.

Question

On the moon, where the local gravity has a magnitude of g=1.6 m/s^2, an astronaut jumps off the edge of a crater rim. It takes her 7.2 seconds to free fall to the crater floor.

a) How high is the crater wall?

b) What is the astronaut's velocity when she is halfway down the fall?

c) What is the astronaut's impact velocity on the crater floor?

Answer 1

a) How high is the crater wall?

height = H = ½gt² = ½(1.6)(7.2)² = 41.472 m = 41.5 m (rounded to 2 significant figures)

b) What is the astronaut's velocity when she is halfway down the fall?

v = √(2gx) where x = ½H (H = the height from part a)

so v = √(2g(½H)) = √(g×H) = √(1.6H) = √(1.6 × 41.472) = 8.1 m/s (rounded to 2 significant figures)

(Note: I read "halfway down" as half the total distance)

c) What is the astronaut's impact velocity on the crater floor?

v = gt = (1.6)(7.2)

or

v = √(2gH) = √(3.2H)

both give the same answer (as they should):

v = 11.52 m/s = 11.5 m/s (rounded to 2 significant figures)

Answer 2

Let's break down the problem step by step:

a) How high is the crater wall?

We can use the formula for free fall in the Moon's gravity to find the height (h) of the crater wall:

h = (1/2) * g * t^2

Where:

h is the height of the crater wall.

g is the Moon's gravity, which is 1.6 m/s².

t is the time it takes to free fall, which is 7.2 seconds.

Plug in the values:

h = (1/2) * 1.6 m/s² * (7.2 s)^2

h = (0.8 m/s²) * (51.84 s^2)

h = 41.472 meters

So, the height of the crater wall is approximately 41.472 meters.

b) What is the astronaut's velocity when she is halfway down the fall?

The astronaut is halfway down the fall when she has fallen half of the height of the crater wall, which is h/2. We can use the following formula to find her velocity at this point:

v = g * t

Where:

v is the velocity.

g is the Moon's gravity, which is 1.6 m/s².

t is the time it takes to reach halfway, which is half of the total time, 7.2 s / 2 = 3.6 s.

Plug in the values:

v = 1.6 m/s² * 3.6 s

v = 5.76 m/s

So, the astronaut's velocity when she is halfway down the fall is 5.76 m/s.

c) What is the astronaut's impact velocity on the crater floor?

The impact velocity can be found using the formula:

v = g * t

Where:

v is the impact velocity.

g is the Moon's gravity, which is 1.6 m/s².

t is the total time it takes to free fall, which is 7.2 seconds.

Plug in the values:

v = 1.6 m/s² * 7.2 s

v = 11.52 m/s

So, the astronaut's impact velocity on the crater floor is 11.52 m/s.