Velocity & Distance of Long Jumper on the Moon

In summary, the long jumper had an initial velocity of 10 m/s in the horizontal direction and an initial vertical velocity of 4 m/s. He would be able to jump 8.12 meters on the moon, assuming the only known variables are a horizontal initial velocity of 10 m/s and a vertical acceleration of 1.63 m/s^2. It would take him a total of 0.82 seconds to complete the jump.
  • #1
aLiase
3
0

Homework Statement


Long jumper jumps 8.12 m, reaching a height of 0.84 m half way through his jump. What was his velocity as he left the ground? Also, how far would he be able to jump on the moon (g = 1.63 m/s^2) and how much time would be spend off the lunar surface.

Homework Equations



d = v1 + at^2 / 2
v = d/t

The Attempt at a Solution



Ok, so I got the answer for the first part, but I just need a recheck from someone, The initial velocity as the jumper left the ground is 10 m/s in the horizontal direction and 0 in the vertical direction? The reason that I'm not sure of this answer is because when I find the angle (22 degrees) the answer becomes 9.27 m/s.

Now the second part is what I'm having problems in because the only variables known are the following:

Horizontal Direction:
V1 = 10 m/s
a = 0 m/s^2

Vertical Direction:
V1 = 0 m/s
a = 1.63 m/s^2

I also got the time from the first part which would be 0.82 seconds, but since the gravity/acceleration is different from Earth shouldn't it take longer for the jumper to go from one point to another?
 
Last edited:
Physics news on Phys.org
  • #2
You're missing a t in your equation for d

The initial velocity as the jumper left the ground is 10 m/s in the horizontal direction and 0 in the vertical direction?

So he...jumps in a straight line, skidding along the ground? I believe they call that running(harhar *crickets chirp*)The angle for that would be 0, so I'm not sure how you found 22 degrees from that, unless you did two different approaches, in which case your answers contradict

And then for some reason on the moon you switched it and he jumps straight up. Although I think that's a typo, it's still the same issue with the other case
 
  • #3
Ok, this is how I did it step by step.

First I found the time it toke from the ground to the maximum height using:

Vertical direction:
d = v1 + a(t)^2 / 2
0.82 = 0 + 9.81(t)^2 / 2
0.82 / 4.905 = t^2
t = 0.41
t(total) = 0.82
Then I multiply that by 2 to get the time it takes for him to jump from one point to the other.

Now I get the initial velocity since I have time I do:
Horizontal direction:
v = d / t
v = 8.12 / 0.82
v = 10 m/s

Then I used the equation v(f)^2 = v(i)^2 + 2ad to find the final velocity in the vertical direction:
v(f)^2 = 0 + 2(9.81)(0.84)
v(f) = sqrt(2(9.81)(0.84))
v(f) = 4 m/s

Then I used Tan(theta) = vertical / horizontal:
theta = tan^-1 (4 / 10/)
theta = 22 degrees

And that how I got the 22 degrees
 
  • #4
Why are you assuming the initial velocity in the y direction is 0? He would never leave the ground

The reason you get an answer that kind of makes sense is because you forgot to include the negative when dealing with his vertical acceleration from gravity, so you're saying he starts with no initial vertical velocity, yet has a final vertical velocity of 4 m/s

So he falls up?
 

What is the velocity of a long jumper on the moon?

The velocity of a long jumper on the moon depends on several factors, such as the force of their jump, the angle of their jump, and the lunar gravity. However, on average, the velocity of a long jumper on the moon is about 1.6 times slower than on Earth due to the moon's weaker gravitational pull.

How does the distance of a long jump on the moon compare to a long jump on Earth?

The distance of a long jump on the moon is significantly greater than on Earth due to the moon's lower gravity. On Earth, an average long jump distance is around 8 meters, while on the moon, it could be up to 13 meters.

Why do long jumpers wear special suits on the moon?

Long jumpers wear special suits on the moon to help them adjust to the lunar gravity and to protect their bodies from the harsh environment. These suits also have special features such as extra padding and grip to assist with the jump.

Can a long jumper break a world record on the moon?

Technically, yes, a long jumper could break a world record on the moon. However, it would not be considered an official world record as the conditions on the moon are significantly different from those on Earth.

How does the distance and velocity of a long jump on the moon affect the jumper's performance?

The lower gravity and slower velocity on the moon allow for longer and higher jumps, which can potentially result in a better performance for the long jumper. However, the lack of air resistance on the moon may also affect the jumper's stability and control in the air.

Similar threads

  • Introductory Physics Homework Help
Replies
3
Views
568
  • Introductory Physics Homework Help
Replies
11
Views
1K
  • Introductory Physics Homework Help
Replies
6
Views
177
  • Introductory Physics Homework Help
Replies
30
Views
1K
  • Introductory Physics Homework Help
2
Replies
46
Views
2K
  • Introductory Physics Homework Help
2
Replies
38
Views
1K
  • Introductory Physics Homework Help
Replies
5
Views
1K
Replies
6
Views
746
  • Introductory Physics Homework Help
Replies
2
Views
607
  • Introductory Physics Homework Help
Replies
5
Views
960
Back
Top