# Dynamics/Kinematics Question

Hey,
An object is fired up a frictionless ramp 65 degrees to the horizontal with an initial velocity of 35 m/s, how long does the object take to return to the starting point.

What I did was:

cos 23 * 35m/s = Vyo
Vyo = 31.72 m/s

Vf = Vo + at
0 m/s = 31/72 m/s + (9.8m/s^2)(t)
t = 3.24s

Then doubled time for down to equal: 6.5s

The answer in the key is 7.9s.
What did I do wrong here?

Thanks,

First thing I would do is draw a diagram. I would define a coordinate system in which the x-axis is parallel to the surface of the plane. That way all my calculations will deal with breaking components into the x-direction. Next I would use F=ma to calculate the acceleration of the object. Then apply projectile motion equations to calculate the time.

I'm still getting 6.5s as an answer :/

Starting with F=ma. The only force that is going to cause an acceleration is gravity (if we use the coordinate system I described).

F = ma
mgsin65 = ma
a = gsin65

Vf = Vi + at
0 = 35 m/s + (gsin65)t
t = 35/gsin65
multiply it by 2 to get whole time
t = 70/gsin65
t = 7.88 seconds.

ah,
that makes sense now
thanks very much