How Fast Was the Ball Going When It Left the Incline?

[kofmelk]

Homework Statement

A ball rolls off an incline plane on top of a 1m high table and strikes the floor 62.5cm from the edge of the table. What was the velocity of the ball just as it left the incline plane?

The incline is given as 30 degrees.

I've put my frame of reference at the point where the ball is at the edge of the table about to fall off.

llllll \
llllll\\\
llllll\\\\
llllll 30\o
1ml--- l
llllllllllllllllll
llllllllllllllllll
llllll____l______________

Homework Equations

1. Position final = Position initial + (Velocity initial * time) + (1/2 Acceleration * time^2)
2. Velocity final = Velocity initial + (Acceleration * time)

The Attempt at a Solution

Since my frame of reference is placed where it is, in the x direction the acceleration is 0 as well as the initial position. So formula 1 in the x-direction boils down to:

.625m = (Velocity initial * time)

Or in other words:

Vi = .625/t

I tried to solve for t in the y-direction but that's where I got stuck. It travels down the ramp first so its initial velocity and position as well as the final velocity are unknown.

Stuck. Thanks for any and all help.

 

[tiny-tim]

call the initial speed v, and split it into x and y components

its initial velocity and position as well as the final velocity are unknown

No.

Its initial position is x = 0, y = 1.

Its initial speed is unknown, so call it v.

Its initial direction is known: 30º to the x-axis.

Split the velocity into x and y components.

Do the y-direction first, and work out the time to reach y = 0 (it'll involve v).

Then use that time to work out the x distance traveled in that time. I'll involve v, and you can put it equal to 0.625!