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Jason has 13720 J of gravitational potential energy standing at the top of a cliff over the lake. If he jumps off the cliff and falls into the water below, how much kinetic energy will he have when he reaches the surface of the water? Explain.

He comes to a stop 5 m beneath the surface of the lake. With what force does the water push on him while stopping him?

Sagot :

The conservation of energy and Newton's second law allows us to find the results about Jason's falling motion are;

  • The energy when reaching the water is K = 13720 J
  • The average force of the water to stop it is: F = 2744 N

Energy conservation.

The conservation of energy is one of the most important principles of physics, stable that if there is no friction force, mechanical energy is conserved at all points.

Mechanical energy is the sum of kinetic energy plus potential energy.

Let's look for the energy at two points

Starting point. Get higher.

         Em₀ = U = 13720 J

Final point. Lower down.

         [tex]Em_f[/tex] = K

Friction in the air is negligible, so energy is conserved.

          [tex]Em_o= Em_f[/tex]

          K = 13720J

Kinematics and Newton's law.

They indicate that it stops 5m under the water, if we assume that the water acts with a constant force, we can use kinematics and Newton's second law to find this force.

The kinematics expression to find the acceleration is

            v² =v₀² – 2ay

When it stops the speed is zero.

            [tex]a = \frac{v_o^2}{2y}[/tex]  

 

Newton's second law is:

           F = ma

           F = m ( [tex]\frac{v_o^2}{2y}[/tex] )

The expression for the kinetic energy is:

          K = ½ m v₀²

          [tex]v_o^2 = \frac{2K}{m}[/tex]  

Let's substitute.

           F = [tex]m (\frac{2K}{m}) \frac{1}{2y}[/tex]  

           [tex]F= \frac{K}{y}[/tex]  

Let's calculate.

           F= [tex]\frac{13720}{5}[/tex]  

           F = 2744N

In conclusion using conservation of energy and Newton's second law we can find the results about Jason's falling motion are;

  • The energy when reaching the water is K = 13720 J
  • The average force of the water to stop it is: F = 2744 N

Learn more about energy here:  brainly.com/question/14274074

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