In a local bar, a customer slides an empty beer mug down the counter for a refil

Question

In a local bar, a customer slides an empty beer mug down the counter for a refill. The height of the counter is h. The mug slides off the counter and strikes the floor at distance d from the base of the counter.

(a) With what velocity did the mug leave the counter? (Use any variable or symbol stated above along with the following as necessary: g.) vxi =

(b) What was the direction of the mug's velocity just before it hit the floor? (Use any variable or symbol stated above as necessary.) = below the horizontal

Explanation / Answer

a) here , as the height of counter is h

time taken for the mug to fall , t = sqrt(2h/g)

Now, for the initial speed in x direction

vxi = d/t

vxi = d/sqrt(2h/g)

vxi = d * sqrt(g/(2h))

b) let the velocity is vf

vy = g * t

vy = g * sqrt(2h/g) = sqrt(2gh)

tan(theta) = vy/vx

tan(theta) = (sqrt(2gh))/(d/sqrt(2h/g))

tan(theta) = 2h/d

theta = arctan(2h/d) below horizontal

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