Assume you have a person with a mass of 65 kg riding a skateboard down a ramp. While they are still 4.8 m high, they are traveling at a speed of 8.0 m/s.
a) Calculate the Eg. [write here)
b) Calculate theEk [write here]
c) Calculate the Etotal. [write here]
d) If the ramp had a total height of 8.0 m, what would be their Eg, Ek, and Etotal at that height?

a) Eg = 3,060.72 j

b) Ek = 2,080 j

c) Etotal = 5,140.72 j

d) Eg = 5,140.2 j

Ek = 0 j

Etotal = 5,140.2 j

Explanation:

The given parameters of the person riding the skateboard are;

The mass of the person, m = 65 kg

The height of the person (above ground level), h = 4.8 m

The speed at which the person is traveling, v = 8.0 m/s

a) The gravitational potential energy, Eg = m·g·h

Where;

m = The mass of the object at the given height = 65 kg

g = The acceleration due to gravity, g ≈ 9.81 m/s²

h = The height by which the object is elevated = 4.8 m

∴ Eg = 65 kg × 9.81 m/s² × 4.8 m = 3,060.72 joules

The gravitational potential energy, Eg = 3,060.72 J

b) The kinetic energy, Ek, is given as follows;

Ek = 1/2·m·v²

Where;

v = The velocity of the object = 8.0 m/s

∴ Ek = 1/2 × 65 kg × (8.0 m/s)² = 2,080 joules

The kinetic energy, Ek = 2,080 J

c) The total mechanical energy, Etotal = Eg + Ek

∴  Etotal = 3,060.72 j + 2,080 j = 5,140.72 J

The kinetic energy, Ek = 5,140.72 J

d) If the ramp had a total height of 8.0 m, we have;

At the 8.0 m height

Etotal = Eg(max), Ek = 0 j

With the given values, we get;

Eg(max) = 65 kg × 9.81 m/s² × 8 m = 5,101.2 joules = Etotal

Eg(max) = 5,101.2 j

Etotal = 5,101.2 j

Ek = 0 j

However, using only the values in the question with the assumption that all things being equal, we have;

Etotal = Constant = 5,140.72 j

Eg a the max height, 8.0 m = Eg(max) = Etotal = 5,140.2 j

Ek = 0 j

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