In a local bar, a customer slides an empty beer mug down the counter for a refill. The height of the counter is 1.18 m. The mug slides off the counter and strikes the floor 1.20 m from the base of the counter. With what velocity did the mug leave the counter? What was the direction of the mug's velocity just before it hit the floor?

Question

In a local bar, a customer slides an empty beer mug down the counter for a refill. The height of the counter is 1.18 m. The mug slides off the counter and strikes the floor 1.20 m from the base of the counter.  With what velocity did the mug leave the counter? What was the direction of the mug's velocity just before it hit the floor?

anonymous · Answer

First find the time it took to fall. This time is independent of the mug's horizontal velocity. The mug has 0 initial velocity in the y direction so the time is found from$$D=1/2*g*t^2=1.18$$The initial velocity will be 1.2/t

When the mug hits the floor it will have the same x velocity as when it left the table. The y velocity will be v=g*t.

You can find the direction of the velocity vector from trigonometry$$\theta=\tan^{-1} (v_y/v_x)$$