"Solving Free-Falling Pole Vaulter Problem

  • Thread starter Pogorz
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In summary, a pole vaulter lands on a soft mat of thickness "h" at a height "H" above the ground. The athlete slows down at a constant rate until his speed is 0 just before he hits the ground. To find the speed and acceleration, the equation v^2=vi^2+2ad was used. The speed before hitting the mat is sqrt19.62H in terms of H, and the acceleration while on the mat is sqrt4.905H/h^2 in terms of H and h. To sketch the graphs for y-t, v-t, and a-t, the vertical position is quadratic in time, the position is linear, and the acceleration is constant. However, the graph
  • #1
Pogorz
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Homework Statement



A pole vaulter comes down after barely clearing the hurdle. the hurdle is at a height "H" above the top of the soft mat on the floor. The mat has a thickness of "h". when the athlete lands on the mat he slows down at a constant rate so that his speed is 0 just before he hits the ground (suppose the mat can be squeezed to a negligible thickness).

a) Find the speed of the athlete just before he hits the mat.
b) Find the acceleration of the athlete while he is in the mat.
c) Sketch the graphs for y-t, v-t, and a-t.

Homework Equations



v^2=vi^2+2ad

The Attempt at a Solution


I solved for Vf (sqrt19.62H) in terms of H, and for acceleration (sqrt4.905H/h^2)in terms of H and h. it says to 'sketch' a graph, so should i just sketch graphs resembling y=x^2, y=x, and y=9.8 for y-t, v-t, and a-t respectively?
 
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  • #2
If by "x" you mean time, yes. The vertical position is quadratic in time, the position is linear and the acceleration is constant. However, note that you graph should come in two pieces. One when he is free fall and the acceleration is - g and one when he has hit the mat and the acceleration is ... ?
 

What is the "Free-Falling Pole Vaulter Problem"?

The Free-Falling Pole Vaulter Problem is a physics problem that involves calculating the trajectory of a pole vaulter as they fall from the top of their jump to the landing pad. It takes into account factors such as the vaulter's initial velocity, the force of gravity, and air resistance.

Why is the "Free-Falling Pole Vaulter Problem" important to study?

Studying the Free-Falling Pole Vaulter Problem allows scientists to better understand the principles of physics, specifically in the area of projectile motion. It also has practical applications in sports, as knowing the trajectory of a pole vaulter can help coaches and athletes improve their technique and performance.

What are the key variables involved in solving the "Free-Falling Pole Vaulter Problem"?

The key variables in solving the Free-Falling Pole Vaulter Problem include the vaulter's initial velocity, the angle at which they release the pole, the vaulter's mass, the force of gravity, and the air resistance. These variables all play a role in determining the vaulter's trajectory and landing point.

What assumptions are made when solving the "Free-Falling Pole Vaulter Problem"?

Some common assumptions made when solving the Free-Falling Pole Vaulter Problem include ignoring any external forces besides gravity and air resistance, assuming a constant acceleration due to gravity, and assuming a constant air density. These simplifications allow for a more straightforward calculation of the vaulter's trajectory.

How can the "Free-Falling Pole Vaulter Problem" be solved?

The Free-Falling Pole Vaulter Problem can be solved using mathematical equations and principles of physics, such as Newton's laws of motion and the equations for projectile motion. It can also be solved using computer simulations and models that take into account the various variables involved.

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