How Far Will a Cart Travel Up a Ramp at Different Angles?

[Tonik]

Homework Statement

A cart is pushed up a ramp with an initial speed v₀=2.5m/s. For this problem, you may assume that the cart is frictionless and the acceleration of the cart a=gsin$$\theta$$.

A) If the angle of the ramp is $$\theta$$=20, what is the maximum distance d that the cart will travel up the ramp?

B) If the angle of the ramp is $$\theta$$=45, what is the maximum distance d that the cart will travel up the ramp?

Homework Equations

v²=v₀²+2a$$\Delta$$X
manipulated to...
(v²-v₀²) / (2a) = $$\Delta$$X

The Attempt at a Solution

A)
9.8sin(20)=3.351797
(0-(2.5)²) / (2(3.351797) = $$\Delta$$X
$$\Delta$$X=10.474 meters

B)
9.8sin(45)=6.9296
(0-(2.5)²) / (2(6.9296) = $$\Delta$$X
$$\Delta$$X=.4509 meters

I was feelin' good about the first answer but the second answer seems too low... did I do these correctly?

 

[Tonik]

Shameless bump.

 

[PhanthomJay]

Shameless bump.

B looks good. Just check your math error in A.

 

[Tonik]

B looks good. Just check your math error in A.

A)
9.8sin(20)=3.351797
(0-(2.5)²) / (2(3.351797) = $$\Delta$$X
$$\Delta$$X=.93234 meters

Fixed, I have no idea how I came up with ~10 meters...
Thanks bud!