Question

A 58 kg pole vaulter falls from rest from a height of 4.9 m onto a foam rubber pad. The pole vaulter comes to rest 0.26 s after landing on the pad.

a) Calculate the athlete’s velocity just be- fore reaching the pad. Answer in units of m/s.

b) Calculate the constant force exerted on the pole vaulter due to the collision.

Answer 1

(a) The athlete's velocity just before reaching the pad is 9.8 m/s

(b) The Constant force exerted on the pole vaulter due to the collision is 37.69 N

(a) To calculate the velocity of the athlete just before reaching the pad, we use the formula below.

Formular:

• mv²/2 = mgh

Simplifying the equation,

• v² = 2gh.................. Equation 1

Where:

• v = Velocity of the athlete before reaching the pad
• g = acceleration due gravity
• h = Height.

From the question,

Given:

• h = 4.9 m
• g = 9.8 m/s²

Substitute these values into equation 2

• v² = 2(4.9)(9.8)

Solve for v

• v² = 96.04
• v = √(96.04)
• v = 9.8 m/s.

(b) To calculate the constant force exerted on the pole vaulter due to collision, we use the formula below.

• F = m(v-u)/t................... Equation 3

Where:

• F = Constant force exerted on the the pole vaulter.
• m = mass of the pole vaulter.
• v = Final velocity
• u = Initial velocity
• t = time.

From the question,

Given:

• m = 58 kg
• v = 9.8 m/s
• u = 0 m/s (From rest)
• t = 0.26 s

Substitite these values into equation 3

• F = (9.8-0)/0.26
• F = 37.69 N.

Hence, (a) The athlete's velocity just before reaching the pad is 9.8 m/s (b) The Constant force exerted on the pole vaulter due to the collision is 37.69 N

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