Dynamics/Kinematics - Jumper beats record jump

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In summary, the jumper needs to jump with a force greater than 1920 N to beat the school's record jump.
  • #1
azukibean
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Homework Statement


The jumper is 60 kg and wants to beat the school's record jump, 1.1 m. She bends her knees a distance of .5 m before jumping. How many Newtons must Fjump be to for her to beat the record?

Homework Equations


ma = ƩF
V2 - V02 = 2a(X - X0)

My teacher stated I would just need these two equations, and that I would use the latter twice.

The Attempt at a Solution


Jumping up to the apex:
02 - 02 = (2)(-10)(1.1)
She jumps up from rest and the velocity of a mass at the apex is zero; right after she jumps, the only force acting on her is gravity, which is -10 m/s2. I assume 1.1 to be X because she can beat the previous runner's score if she jumps 1.1000001 m, essentially 1.1. So in my solution I could say "she has to jump with a force great than _X."

60a = Fjump - 600
I need acceleration from the previous step.

a) I don't know how to work in the .5 m into the equations. Would I add .5 to X? I would still get a nonsensical answer for step 1.
b) What is wrong with step 1's set up?
 
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  • #2
The problem with step 1 is with your definition of "initial". The v0 in your equation is not the speed at the beginning of the jump. It's the launch speed: the speed at the end of the jump, once the jumper's legs are straight and she leaves the ground. And v is the final speed, the speed at the apex, which is 0. So, we have:

v0^2 = -2gh, where h = 1.1 m, the desired height of the jump.

Okay, that's all well and good, and from this we can find the launch speed needed.

How do we get the jump force? That's step 2, where we apply the kinematics equation again. It must be that the acceleration from the net force Fjump - weight, applied over a distance of 0.5 m, gives you a final v that is equal to v0 from step 1. So, in *step 2*, "initial" now means at the beginning of the jump. So v0 = 0, and v = the needed launch speed from step 1, and d = 0.5 m. From this you can solve for 'a', which gives you Fnet.
 
  • #3
Cepheid variable!
---
Straight legs:
v0^2 = 2*-10*1.1
v0 = 4.69

Bent:
4.69^2 - 0^2 = 2*.5*a
a = 21.996

60*22 = F(jump) - 600
F(jump) = 1920 N
---
Thanks!
 

1. How is the record jump in dynamics/kinematics measured?

The record jump in dynamics/kinematics is measured by calculating the distance the jumper travels from the takeoff point to the landing point. This distance is measured using specialized equipment such as high-speed cameras and laser measuring devices.

2. What factors affect the distance of a jump in dynamics/kinematics?

The distance of a jump in dynamics/kinematics is affected by various factors including the speed and angle of takeoff, the height of the jump, and the aerodynamics of the body in motion. Other environmental factors such as wind speed and direction can also impact the distance of a jump.

3. Can a jumper beat their own record jump?

Yes, a jumper can beat their own record jump by improving their technique and increasing their physical capabilities. By analyzing and adjusting various factors such as speed, angle, and height, a jumper can potentially surpass their previous record jump.

4. How does the height of a jump affect the record in dynamics/kinematics?

The height of a jump can greatly impact the record in dynamics/kinematics. The higher the jump, the longer the time the jumper has in the air, allowing them to cover more distance. However, a higher jump also requires more energy and power, which may affect the overall distance of the jump.

5. Is there a limit to how far a jumper can jump in dynamics/kinematics?

Yes, there is a physical limit to how far a jumper can jump in dynamics/kinematics. This limit is determined by various factors such as the strength and physical capabilities of the jumper, as well as external factors such as wind and surface conditions. However, with advancements in technology and training techniques, this limit may continue to be pushed by athletes in the future.

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