Speed of toy car at highest point after leaving curved track

[Michele Nunes]

Homework Statement

A toy car coasts along the curved track shown. The car has initial speed V_A when it is at point A at the top of the track, and the car leaves the track at point B with speed V_B at an angle θ above the horizontal. Assume that energy loss due to friction is negligible.

Determine the speed of the car when it is at the highest point in its trajectory after leaving the track, in terms of V_B and θ. Briefly explain how you arrived at your answer.

Homework Equations

The Attempt at a Solution

Okay so conceptually I think I understand how to do the problem. At point A, all potential energy, at point B, almost all kinetic energy. Then when the car leaves point B, energy is lost due to the downward force of the car's weight, so I want to find the work done by the car's weight and then subtract that from the original amount of energy the car possessed and then go from there. But in terms of how this plays out in the actual equations, I have no idea. I'm not sure where to start in terms of the setting equations equal to each other and how exactly to set that up.

 

[JeremyG]

Determine the speed of the car when it is at the highest point in its trajectory after leaving the track, in terms of VB and θ. Briefly explain how you arrived at your answer.

If this is all you need to find then there's no need for considerations of energy, work or whatever goes on at the curved track. It is simply a projectile motion question. What is the speed of a projectile at its highest point? Think in terms of the vertical and horizontal speeds

 

[Michele Nunes]

If this is all you need to find then there's no need for considerations of energy, work or whatever goes on at the curved track. It is simply a projectile motion question. What is the speed of a projectile at its highest point? Think in terms of the vertical and horizontal speeds

But how would I do that if I don't know any other variable? Like I don't know time or acceleration or displacement so how would I get the speed only in terms of V_B and θ?

 

[JeremyG]

1. For projectile motion, neglecting air resistance, the horizontal component of the velocity remains constant. The only force acting on the projectile during this parabolic motion is its own weight, in the vertical direction.

2. At its highest point, what is its vertical and horizontal speed? You do not need time, acceleration nor displacement to come up with an expression of the velocity at the highest point.

 

[Michele Nunes]

1. For projectile motion, neglecting air resistance, the horizontal component of the velocity remains constant. The only force acting on the projectile during this parabolic motion is its own weight, in the vertical direction.

2. At its highest point, what is its vertical and horizontal speed? You do not need time, acceleration nor displacement to come up with an expression of the velocity at the highest point.

Oh yes okay, I was definitely over thinking this, thank you!

 

[JeremyG]

No problem! Glad to help! :)