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)

a) Eg = 3,060.72 j

b) Ek = 2,080 j

c) Etotal = 5,140.72 j

Explanation:

The given parameters are;

The mass of the person, m = 65 kg

The height of the person, h = 4.8 m

The speed of the person, v = 8.0 m/s

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

Where;

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

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

Eg = 3,060.72 j

b) The kinetic energy, Ek = 1/2·m·v²

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

Ek = 2,080 j

c) The constant total Mechanical Energy, Etotal = Eg + Ek

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

Etotal = 5,140.72 j.

the minimum constant speed at which she can catch the train is 2.7 m/s

given:

acceleration = 0.6

time = 4.5 s

to find:

velocity = ?

formula used:

from 1st kinematic equation we get,

v = u + at

u = initial speed of train = 0 m/s

v = final speed of the train

a = acceleration of the train

t = time

solution:

from 1st kinematic equation we get,

v = u + at

u = initial speed of train = 0 m/s

v = final speed of the train

a = acceleration of the train

t = time

v = 0 + (0.6 × 4.5)

v = 2.7 m/s

the minimum constant speed at which she can catch the train is 2.7 m/s