The motion of a skateboarder along and above a ramp

[StrugglingStudent123]

Homework Statement

A skateboarder starts at the bottom of a ramp (E1) with a speed of 7.2 m/s. She rolls up the ramp, slowing down with an acceleration of -6.1 m/s², and finally leaves the end of the ramp (E2), which is 1.2 m above the ground. She travels through the air, reaching a maximum height (E3—this is made as an event for practice purposes) with a speed of 4.1 m/s at a height of 1.7 m. She lands on the top of the next ramp (E4), which has a height of 1.0 m. She then rolls down that ramp, speeding up with an acceleration of 6.5 m/s² till the end of the ramp, which is 2.5 m long (E5).

I need help with this one question: what is the velocity at event 2

Relevant Equations

the big 5 equation, uniform motion and projectile motion

I have tried to use the projectile motion to find Vx and Vy, however since the angle isn't given, I don't think this problem can be solved with only motion formulas (I did solve it with energy formulas).

 

[berkeman]

Welcome to PF. The problem statement is confusing to me, especially this part:

She travels through the air, reaching a maximum height (E3—this is made as an event for practice purposes) with a speed of 4.1 m/s at a height of 1.7 m.

Is there a diagram that goes with this problem? You can upload it using the "Attach files" link below the Edit window. And if that is her "speed" at her maximum height, which direction is she traveling at that point?

Also, for your Relevant Equations, are there any Energy equations that you think might be pretty handy?

 

[haruspex]

Homework Statement: A skateboarder starts at the bottom of a ramp (E1) with a speed of 7.2 m/s. She rolls up the ramp, slowing down with an acceleration of -6.1 m/s², and finally leaves the end of the ramp (E2), which is 1.2 m above the ground. She travels through the air, reaching a maximum height (E3—this is made as an event for practice purposes) with a speed of 4.1 m/s at a height of 1.7 m. She lands on the top of the next ramp (E4), which has a height of 1.0 m. She then rolls down that ramp, speeding up with an acceleration of 6.5 m/s² till the end of the ramp, which is 2.5 m long (E5).

I need help with this one question: what is the velocity at event 2
Relevant Equations: the big 5 equation, uniform motion and projectile motion

I have tried to use the projectile motion to find Vx and Vy, however since the angle isn't given, I don't think this problem can be solved with only motion formulas (I did solve it with energy formulas).

It is unclear whether mechanical energy is conserved up to E2. If it is, the state at E3 is overspecified. (Indeed, based on the other information the height should be 1.78m.)
I suggest working backwards from the E3 information.