Moon Jumping: Calculating Acceleration, Range and Time

[veronicak5678]

Homework Statement

On the surface of the moon, an astronaut jumps with a speed of 1.0 m/s at an angle of 30 degres above the horizon. A max height of .78 m is reached.

a- What is the acceleration of gravity on the moon?
b- Determine the horizontal range.
c- How much time did this displacement take?

Homework Equations

at/2 = v initial (sin angle)

displacement =((v initial) ^2 (sin angle))/a

ymax = (v initial)^2 / 2a

The Attempt at a Solution

question a-
2a(.78m) = 1)(1/2)

acceleration is .064 m/s^2

question b-
displacement = (1)(sin 60)/.064
displacement = 13.53 m

question c-
t = .5 m/s / .032 m/s^2
t = 15.62 s


Have I made a mistake? I thought gravity on the moon was 1.6 m/s^2, and my teacher usually uses examples that work out correctly.

 

[anathema]

Hi, great job on attempting the problem! However, there are a few mistakes in your calculations.

For question a, you are correct that the acceleration due to gravity on the moon is 1.6 m/s^2. This can be found using the formula g = G*M/r^2, where G is the universal gravitational constant, M is the mass of the moon, and r is the distance from the center of the moon to the surface.

For question b, the horizontal range is not calculated using the formula you used. Instead, you can use the formula d = v0 * t, where d is the horizontal distance, v0 is the initial horizontal velocity, and t is the time. Since the initial horizontal velocity is 1.0 m/s and the time is 15.62 seconds, the horizontal range is 15.62 meters.

For question c, you have used the wrong values in your calculation. The correct formula to use is t = v0 * sin(angle) / g, where v0 is the initial vertical velocity, angle is the angle above the horizon, and g is the acceleration due to gravity. Plugging in the correct values (1.0 m/s for v0, 30 degrees for angle, and 1.6 m/s^2 for g), we get t = 2 seconds.

Overall, your approach was correct, but be careful to use the correct formulas and values in your calculations. Keep up the good work!

 

[baba89]

Your calculations are correct. The acceleration of gravity on the moon is approximately 1.6 m/s^2, so it is possible that your teacher made a mistake in the homework statement or used a different value for the acceleration of gravity. It's always a good idea to double check your calculations and assumptions, especially when they seem to be different from what you expect. Keep up the good work!