Question

A 65 kg diver stands still on a tower, 10.0 m above the water. (a) Calculate the gravitational potential energy of the diver, relative to the height of the water. Assume the gravitational field constant is 9.8 N/kg (b) The diver reaches the surface of the water at a speed of 14 m/s. Calculate the diver’s kinetic energy. (c) Compare your answers to (a) and (b). Explain your comparison using concepts learned in this course. Assume there is no air resistance during the dive. (d) Calculate the speed of the diver 5.0 m above the water.

Answer 1

Answer:

Explanation:

a) PE = mgh = 65(9.8)(10) = 6370 J

b) KE = ½mv² = ½(65)14² = 6370 J

c) Potential energy has converted to kinetic energy with zero loss to friction.

d) 6370/2 = ½(65)v²

             v = √(6370/65)

             v = √98 m/s  or approximately 9.9 m/s

Only half of the potential energy was converted to kinetic energy.

Answer 2

A. The gravitational potential energy of the diver is 6370 J

B. The diver’s kinetic energy is 6370 J

C. The gravitational potential energy and the kinetic energy of diver is the same.

D. The speed of the diver 5.0 m above the water is 9.9 m/s

A. Determination of the gravitational potential energy.

• Mass (m) = 65 Kg

• Gravitational field constant (g) = 9.8 N/kg

• Height (h) = 10 m

• Potential energy (PE) =?

PE = mgh

PE = 65 × 9.8 × 10

PE = 6370 J

B. Determination of the kinetic energy

• Mass (m) = 65 Kg

• Velocity (v) = 14 m/s

• Kinetic energy (KE) =?

KE = ½mv²

KE = ½ × 65 × 14²

KE = 6370 J

C. Comparison of the gravitational potential energy and the kinetic energy

Potential energy (PE) = 6370 J

Kinetic energy (KE) = 6370 J

From the above, we can see that the gravitational potential energy and the kinetic energy of the diver is the same during the dive since air resistance is negligible.

D. Determination of the speed of the diver at 5 m above the water

We'll begin by calculating the gravitational energy.

• Mass (m) = 65 Kg

• Gravitational field constant (g) = 9.8 N/kg

• Height (h) = 5 m

• Potential energy (PE) =?

PE = mgh

PE = 65 × 9.8 × 5

PE = 3185 J

Finally, we shall determine the velocity.

• Kinetic energy (KE) = potential energy = 3185 J

• Mass (m) = 65 Kg

• Velocity (v) =?

KE = ½mv²

3185 = ½ × 65 × v²

3185 = 32.5 × v²

Divide both side by 32.5

v² = 3185 / 32.5

Take the square root of both side

v = √(3185 / 32.5)

v = 9.9 m/s

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