Winning at Amusement Park Game: Varying Velocities

[quick]

One game at the amusement park has you push a puck up a long, frictionless ramp. You win a stuffed animal if the puck, at its highest point, comes to within 10 cm of the end of the ramp without going off. You give the puck a push, releasing it with a speed of 5.0 m/s when it is 8.50 m from the end of the ramp. The puck's speed after traveling 3.0 m is 4.0 m/s.

Am I a winner or not?

Please explain how to do this problem. thanks in advance.

 

[robphy]

Here's something to start you off.

Along the ramp, the puck experiences a constant acceleration. (Why?)
With your data (namely, the velocity and position at two different events), you can determine this acceleration.
Given the velocity at your final event, you can determine the position of that final event.

You can also do this using "conservation of energy".

 

[quick]

so i use the equation:
v_f^2 = v_i^2 + 2a(x_f - x_i)
and solve for a?

i tried with the following values:

4^2 = 5^2 + 2a(5.5 - 8.5) {this part was kind of confusing since the way they give the positions is '8.5m from the end of the ramp' and then 'after traveling 3.0m') after solving for a i got .84

 

[robphy]

That's a good equation to use.

Assuming "up the ramp" to be the positive direction, I would have expected the component of acceleration along the ramp to be negative. Try calling the "end of the ramp" "0 cm" and the initial position "-850. cm".

 

[quick]

awesome i got it. thanks for your help!