The Conservation of Mechanical Energy help?

KEbottom = PEtop

(1/2)mv^2 = mgh

mass cancels out

(1/2)v^2 = gh

solve for h

((1/2)v^2)/g = h

((1/2)(5.4m/s)^2)/(9.8m/s^2) = h

h = 1.49m

The conservation of energy gives that E = T + V at all times, where E is the total energy, T is the kinetic energy, and V is the potential. At the start, the skateboarder has T1 = 1/2mv^2 and V1=0, at the peak of his run, he has T2=0 and V2 = mgh, then,

E = T1 + 0 = 0 + V2

T1 = V2

1/2mv^2 = mgh. Solving for h:

h = v^2/(2g). Where the v here is the initial velocity, and g is the acceleration due to gravity.

Okay. Well Kinetic Energy (energy of a moving object that has mass) is equal to 1/2mv^2 (one half mass x (velocity squared)).

So, solving this equation we would have to say that at the highest point of the other side of the ramp, the skate boarder would no longer have Kinetic Energy. We know this because when an object is moving straight up (and in this problem I am assuming the skate boarder is) its velocity becomes zero upon reaching the highest point. Just imagine throwing a ball straight up, it will stop before it changes direction and comes back down. So knowing this we know that the velocity at the highest point will be zero. Since the velocity of the skate boarder is 0 and if you plug zero 0 into the equation for Kinetic energy your answer will be 0. So, Kinetic Energy at the highest point is 0.

Since energy is always conserved, the starting Kinetic energy should equal the final Potential energy. Potential energy expressed by the equation PE=mgh (mass x gravity x height above the zero level). The zero level is going to be the height from which the skate boarder started from on the left side of the ramp.

Next, we know Total Energy from the start equals Total Energy at the end. Total energy is expressed by the equation TE=KE+PE (total energy = kinetic energy + potential energy). Since the object starts at the zero level, h in the PE equation will equal zero. So PE equals zero for TEa (total energy at the start); TEa=KE. And since Kinetic energy is zero at the end KE drops out of TEb (total energy at the end) so TEb=PE. Now since TEa=TEb and TEa=KE and TEb=PE then KE=PE. Or, 1/2mv^2=mgh.

Now to try and make this look prettier.

TEa=KE+PE

TEa=1/2mv^2+mgh

TEa=1/2m(5.4)^2 + m9.8(0)

TEa=14.58m

TEb=KE+PE

TEb=1/2mv^2+mgh (v=0 because its at its highest point)

TEb=1/2m(0)^2 + m(9.8)h

TEb=(9.8)mh

TEa=TEb

(14.58)m=(9.8)mh (m's cancel)

(14.58)/(9.8)=h

h=1.49 meters above the zero level

Hope that makes sense.