Physics moon gravity question

• astru025
In summary, the conversation discusses the calculation of the time in the air for a golf ball hit by Alan Shepherd during Apollo 14 on the Moon. The initial velocity is given as 30m/s at an angle of 15°. The attempted solution uses the equation 30 m/s / 1.6, but fails to take into account the angle of the initial velocity. The correct solution involves dividing the initial velocity into vertical and horizontal components, and using the notes for ballistic motion to calculate the time in the air. The conversation also mentions the lack of air on the Moon, making the question somewhat of a trick question.

Homework Statement

During Apollo 14, Alan Shepherd hit a golf ball on the Moon. If he hit the ball at an angle of 15° and an initial velocity of 30m/s,
what was the time in the air?

Homework Equations

30 m/s / 1.6
So it takes 18.750 seconds to get to the top where you start at 0. Then multiply 18.75 by 2 to get 37.5 so you have total time going down and up,

I got 1.6 cause that is gravity on the moon.
37.5 was the incorrect answer though.

The Attempt at a Solution

37.5 did not prove to be correct.

astru025 said:

Homework Statement

During Apollo 14, Alan Shepherd hit a golf ball on the Moon. If he hit the ball at an angle of 15° and an initial velocity of 30m/s,
what was the time in the air?

Homework Equations

30 m/s / 1.6
So it takes 18.750 seconds to get to the top where you start at 0. Then multiply 18.75 by 2 to get 37.5 so you have total time going down and up,
You are arguing that the ball has an initial velocity of 30m/s and it decelerates at 1.6m/s/s along it's direction of travel, changes direction, and then accelerates back to the ground at the same rate. ... however, this cannot be the case. If it did, then the return journey would put it back on the tee ... but it ended up some distance away. But there is a simpler clue: you haven't used the angle part of the initial velocity.

Take another look at your notes for ballistic motion.
When the ball hits the top of it's trajectory, only the vertical component is zero - the horizontal component is constant for the entire motion.

astru025 said:

Homework Statement

During Apollo 14, Alan Shepherd hit a golf ball on the Moon. If he hit the ball at an angle of 15° and an initial velocity of 30m/s,
what was the time in the air?

Homework Equations

30 m/s / 1.6
So it takes 18.750 seconds to get to the top where you start at 0. Then multiply 18.75 by 2 to get 37.5 so you have total time going down and up,

I got 1.6 cause that is gravity on the moon.
37.5 was the incorrect answer though.

The Attempt at a Solution

37.5 did not prove to be correct.

Hah! Trick question! There is no air on the moon!

But seriously, what happened to the angle of 15 degrees? Don't you think that makes a difference in how long the golf ball stays aloft?

In cases like this when the initial velocity has an angle theta from the horizontal you need to divide the initial velocity into vertical and horizontal components.

The correct answer can be found using the equation t = 2v0sin(theta)/g, where t is the time in the air,
v0 is the initial velocity, theta is the angle of launch, and g is the acceleration due to gravity on the moon (1.6 m/s^2).
Plugging in the given values, we get t = 2(30m/s)sin(15°)/1.6m/s^2 = 2.5 seconds. Therefore, the ball was in the air for 2.5 seconds before landing back on the surface of the moon.

What is the moon's gravity?

The moon's gravity is approximately 1/6th of Earth's gravity, which means that objects on the moon weigh about 16.5% of what they would weigh on Earth.

Why is the moon's gravity weaker than Earth's?

The moon's weaker gravity is due to its smaller mass and size compared to Earth. The force of gravity is directly proportional to an object's mass and inversely proportional to the square of its distance from another object.

How does the moon's gravity affect objects?

The moon's gravity affects objects by pulling them towards its center. This causes objects to have less weight on the moon compared to Earth, and also causes tides on Earth's oceans.

Can humans live on the moon with its weaker gravity?

Humans can potentially live on the moon with its weaker gravity, but it would require adaptations to compensate for the effects of low gravity on the human body, such as muscle and bone loss.

Does the moon's gravity affect Earth's gravity?

Yes, the moon's gravity does affect Earth's gravity. The gravitational pull of the moon causes Earth's oceans to bulge, creating tides. The moon's gravity also has a small effect on Earth's orbit around the sun.

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