Daredevil motorcycle max height

[Leid_X09]

Homework Statement

A daredevil on a motorcycle leaves the end of a ramp with a speed of 39.5 m/s as in Figure P5.23. If his speed is 38.0 m/s when he reaches the peak of the path, what is the maximum height that he reaches? Ignore friction and air resistance.

Homework Equations

Eo = mgy

Ek = 1/2mv^2

The Attempt at a Solution

I don't even know where to begin. I need someone to cue me on what equation i should be using because frankly I can't even fathom. I thought perhaps Eo=Ek, but I'm not sure if this is it.

 

[Epsillon]

Alright so in the beginning the motocycle has Ek only; however, when it reaches the top it gains some Ep therefore some Ek is transformed into Ep due to conservation of energy.

So

E_kinitial=E_kfinal+E_p

Ep = mgy

Ek = 1/2mv^2

so

1/2m(39.5)^2 = 1/2m(38)^2 + m(9.8)y

Now u can cross out the ms by factoring m from both sides and deviding boths sides by m.
1/2(39.5)^2 = 1/2(38)^2 + (9.8)y

y=0.1102556674m

 

[baba89]

I would suggest that the appropriate equation to use in this situation is the conservation of energy equation, which states that the initial energy (Eo) is equal to the final energy (Ef). In this case, the initial energy would be the kinetic energy (Ek) of the motorcycle rider at the end of the ramp, and the final energy would be the potential energy (mgy) at the peak of the path.

Therefore, we can set up the equation as follows:

Ek = mgy

1/2mv^2 = mgy

We can cancel out the mass (m) on both sides of the equation, leaving us with:

1/2v^2 = gy

To solve for the maximum height (y), we can rearrange the equation to isolate y:

y = 1/2v^2/g

Using the given values of 38.0 m/s for v and assuming a gravitational acceleration of 9.8 m/s^2, we can plug these values into the equation to calculate the maximum height:

y = 1/2(38.0 m/s)^2/9.8 m/s^2

y = 72.65 meters

Therefore, the maximum height that the daredevil reaches is approximately 72.65 meters.

It is important to note that this calculation assumes ideal conditions with no air resistance or friction, so the actual maximum height reached by the daredevil may be slightly different in real life.