Question

Len is a 59 kg pole vaulter and he falls from a peak height of 5.0 meters after pole-vaulting over the crossbar set at that height. He lands on a thick mat and when he first makes contact with the mat, his centre of gravity is only 0.91 meters high. During Len's impact with the mat, it undergoes a maximum compression when his vertical velocity reaches 0 m/s and his centre of gravity is only 0.4 meters high. What is the magnitude (ignore direction) of the average force in Newtons exerted by the mat on Len during this impact?

Answer 1

Initially height of the pole vaulter is h₁=5.0 meters. Just before coming in contact with the mat, the height of the pole vaulter is h₂=0.91 meters. The acceleration of the vaulter during this part of the motion is a₁=-9.8m/s². Assuming the pole vaulter was initially at rest v₁=0. Since acceleration is constant, the motion is governed by the kinematics equations for uniformly accelerated motion. To find the velocity of the vaulter just before hitting the mat we use the following kinematics equation

Substituting values

Consider the second part of the motion, which is the motion of the vaulter when he is in contact with the mat. His height changes from h₂=0.91 meters to h₃=0.40 meters. His velocity changes from v₂=8.953 m/s to v₃=0. The acceleration (a₂) of the vaulter in this part of the motion is given by

Substituting values

There are two forces acting on the vaulter in this part of the motion: gravitational force of the Earth and the force by the mat. The free body diagram is shown below:

By Newton's second law of motion, the net force on vaulter accelerates the vaulter

Substituting values