Can You Win the Puck Game at the Amusement Park?

[barthayn]

Homework Statement

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 5.0m/s when it is 8.5m from the end of the ramp. The puck's speed after traveling 3.0m is 4.0 m/s. Are you a winner?

Homework Equations

vf^2 = vi^2 +2ad
x(t) = 1/2at^2 + vt

The Attempt at a Solution

a = (vf^2-vi^2)/2d
a = (16-25)/6
a = -3/2 m/s/s

x(t) = -3/2t^2 + 5t m
v(t) = -3t + 5 m/s
v(t) = 0 = -3t + 5
t = 5/3

x(5/3) = 26/5 m = 4.16m
df = 8.5 - 4.16
df = 4.3

Therefore, you are not a winner because you are off by a distance of 4.2m before you earn the stuffed animal at the amusement park.

Is this the correct method of doing this question. I feel that I am wrong because in high school it was always winning or going in the basket and not it is not. I believe it is unlikely that the answer will tell us that we are not a winner. Is there anything wrong with my logic process here?

 

[Ignea_unda]

a = (vf^2-vi^2)/2d
a = (16-25)/6
a = -3/2 m/s/s

This is correct.

x(t) = -3/2t^2 + 5t m
v(t) = -3t + 5 m/s
v(t) = 0 = -3t + 5
t = 5/3

Check your relevant equations and your previous work. You have a slight arithmetical error here that makes a very large difference in your final solution.


Your process seems sound, just check your arithmetic. Post again if you want another double check.

 

[barthayn]

This is correct.Check your relevant equations and your previous work. You have a slight arithmetical error here that makes a very large difference in your final solution.Your process seems sound, just check your arithmetic. Post again if you want another double check.

Thanks for pointing that out. I seen a two below the number and thought it was halved. It wasn't. I got it stopping 6.67cm away from the edge, and therefore I am the winner of the stuffed animal correct?

 

[Ignea_unda]

Yes, it looks like that is correct.

 

[rwisz]

Your method is correct and your reasoning is sound. Based on the given information, it appears that you are not a winner because the puck did not come within 10 cm of the end of the ramp without going off. However, it is possible that there may be other factors at play that could affect the outcome. For example, the conditions of the ramp and the puck's trajectory could also impact whether or not the puck would have gone off the ramp. As a scientist, it is important to consider all possible factors and to not jump to conclusions based on limited information. So while your method is correct, it is also important to acknowledge that there could be other factors that may affect whether or not you are a winner in this scenario.