# Standing Jump

1. Dec 11, 2009

### PearlyD

1. The problem statement, all variables and given/known data
An Exceptional standing jump would raise a person 0.80m off the ground. To do this, what force must a 66Kg person exert against the ground? Assume the person crouches a distance of 0.20m prior to jumping, and thus the upward force has this distance to act over before he leaves the ground.

2. Relevant equations

3. The attempt at a solution
Heres what i attempted.
The upward force would be the normal force(Fn) which is the same as the Force of gravity so i caculated that and i got Fg=646.8 the force going down would be the applied force(Fa)
Heres what i got fo far before i got stumped..
Fa-Fn=ma
Fa-646.8=66a

I dont know how i would get acceleration?

2. Dec 11, 2009

### denverdoc

First, The force of the jump must provide an acceleration greater than gravity or he will never leave the ground. One of the more straightforward approaches is that we can equate the work done to the force * displacement (here given as 0.2 meters) with the potential energy given which is the displacement of the center of mass (0.8m) x gravity*mass.

Since you know the force, the acceleration as he straightens his legs can be found.

3. Dec 11, 2009

### PearlyD

What do you mean by work done?
Also do you mean by this equation..
Work done* Displacement(0.2) EQUALS potential energy?
and Potential energy is also 0.80*Gravity*mass?

4. Dec 11, 2009

### denverdoc

Have you covered work? If not we can use a purely kinematics approach. But by work yes the upward force times the displacement over which it acts--as he goes from a crouch to the point at where his feet leave the ground. After that he can exert no more force and he slows due to gravity.

EDIT: But yes, you have almost the right eqns listed. Work=force* displacement=ma* displacement

5. Dec 11, 2009

### PearlyD

No, i havent covered work.
So from crouch to the point where his feet leave the ground i got a force of 129.36N
How would you find the acceleration,to find the Force that he exerts againts the ground?
the only equations i know of at the moment is Fnet=ma and Fg=mg

6. Dec 11, 2009

### denverdoc

Ok, forget work and potential energy.

Lets use kinematics only.

Can you calculate the initial velocity of an object leaving the ground which reaches 0.8meters high?

7. Dec 11, 2009

### PearlyD

To find an initial velocity id either need a Final velocity or a time. and i dont have either.

8. Dec 11, 2009

### denverdoc

No you don't: this is the equation I used in the similar problem which in completeness is

2*a*(displacement)=Vf^2-Vi^2 In both these problems, either initial or final velocity is zero.

You can derive these equations by calculating time, but they are of such usefulness in kinematics, well worth committing to memory. Another tip is that in these types of problems you could have considered the mass at rest at 0.8m hiigh and ask yourself how fast it hits the ground--it is exacty the same problem as asking how fast must it be going leaving the ground to reach a height of 0.8 m.

9. Dec 12, 2009

### PearlyD

Is 2a the same as displacement?

10. Dec 12, 2009

### denverdoc

No the displacement is the distance over which the force acts: the a is acceleration.

This will allow you to get acceleration and hence force like the other problem.

11. Dec 12, 2009

### PearlyD

I used (mass)Gravity)(Displacement)=1/2mV^2
to get a velocity,would that work for this question?

12. Dec 12, 2009

### denverdoc

That works to get the initial velocity. But tere are two displacements in the problem--the first is that of the center of mass as he springs from crouch to leap. The other displacement is that against gravity--how high he flies.

(This is why concept of work would be so useful: force1*displacement1 is equal and opposite to force2 * displacement2). The mass is the same in both cases. So the relative accelerations are proportional to the distance over which the forces act)

13. Dec 12, 2009

### PearlyD

Im starting over again
and im spliting the question in two
first one is the crouch,and im gonna find that force,that he uses to go from crouch to stand.
But what kinematics equation would i use to find acceleration?
I have Vi which is 0 and distance= 0.20 but thats it i dont know what id do?