Zoe, a 55 kg gymnast is performing a vault. She runs toward the vault apparatus

Question

Zoe, a 55 kg gymnast is performing a vault. She runs toward the vault apparatus at a constant velocity of 5 m/s and her center of mass (COM) is 1.0 m above the ground. Her mechanical energies due to her approach velocity and due to her COM position during the approach are completely converted to her total mechanical energy while she is in the air. (a) What is the peak height of Zoe’s COM while she is in the air? (b) What is Zoe’s vertical velocity the instant she lands upright on a mat 0.6 m thick (COM height = 1.6 m from the ground)? (c) The mat compresses to a maximum depth of 0.3 m during Zoe’s landing. At the point of maximum compression of the mat, her vertical velocity reaches zero and her COM is 1.3 m above the ground. What average force did the mat exert on Zoe during the impact?

Explanation / Answer

intially kinetic energgy = 0.5 mv^2

a.) potential energy = K.E + P.E

mgh = 0.5mv^2 + mgh1

9.81*h = 0.5*5^2 + 9.81*1

h = 2.27 m

peak height of Zoe’s COM while she is in the air is 2.27 m

b.) vertical velocity

mgh = 0.5mv^2 + mgh1

9.81*2.27 = 0.5v^2 + 9.81*1.6

v = 3.62 m/s

c.)impact = change in momentum

velocity when COM = 1.3 m

mgh = 0.5mv^2 + mgh1

9.81*2.27 = 0.5v^2 + 9.81*1.3

v = 4.36 m/s

Impulse = change in momentum

I = mv = 55*4.36 = 239.93 kgm/s

Related Questions

Navigate

• Browse (All)
• Browse Z
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.