Question

Suppose a skydiver (mass=75kg) is falling toward the earth when the skydiver is 100m above the earth he is moving at 60m/s at this point calculate the skydivers gravitational potential Energy,kinetic energy, Mechanical energy

Answer 1

PE = 7.4 × 10⁴ J

KE = 1.4 × 10⁵ J

ME = 2.1 × 10⁵ J

Step-by-step explanation:

Given data

mass (m): 75 kg

height (h): 100 m

speed (v): 60 m/s

acceleration due to gravity (g): 9.81 m/s²

Potential energy (PE)

This is the energy due to the position of the skydiver.

PE = m × g × h = 75 kg × 9.81 m/s² × 100 m = 7.4 × 10⁴ J

Kinetic energy (KE)

This is the energy due to the movement of the skydiver.

KE = 1/2 × m × v² = 1/2 × 75 kg × (60 m/s)² = 1.4 × 10⁵ J

Mechanical energy (ME)

The mechanical energy is the sum of the potential energy and the kinetic energy.

ME = PE + KE = 7.4 × 10⁴ J + 1.4 × 10⁵ J = 2.1 × 10⁵ J

Answer 2

Given:

Mass(m)=75kg

Height (h) =100m

v(velocity)=60m/s

a(g)=9.8m/s^2(since it is a free falling object)

Now we know that

v=u+at

We know that

Potential energy=mgh

Where m is the mass

g is the acceleration due to gravity

h is the height above the ground

Substituting the above values we get

Potential energy=75 x 9.8 x 100

=73500N

Now kinetic energy =1/2mv^2

Where m is the mass

v is the velocity

Kinetic energy= 1/2 (75x60 x 60)

Kinetic energy=135000N

Now mechanical energy=

Kinetic energy+ Potential energy

Substituting the values in the above formula we get

Mechanical energy= 73500+135000

=208500N