A gymnast falls from the high bar and lands on a 10 cm thick gymnastics mat. The gymnast strikes the back of his head against the mat during his landing. His head is moving at 7 m/s when it first strikes the mat. The mass of his head is 5 kg. The impact ends when the gymnast's head comes to a stop after deflecting the mat 6.5 cm.
a. How much kinetic energy does the gymnast's head have at the instant just before it contacts the mat?
b. How much work does the mat do to stop the motion of the gymnast's head?
c. What average impact force does the mat exert on the gymnasts head during the impact?
d. Estimate the peak impact force exerted by the mat on the gymnast's head.
e. Estimate the peak acceleration of the gymnast's head.
f. Express this peak acceleration in g's.