Question

n a local coffee shop, a customer slides her empty nitro cold brew downthe counter for a refill. The barista is distracted, and the coffee cup slides offthe counter,initially moving horizontally. The cup travels horizontal distance2mbefore hitting theground.(a)If the height of the counter is4/5m, at what speed was the cup traveling when it leftthe counter

Answer 1

5 m/s

Step-by-step explanation:

Horizontal distance traveled, x = 2 m

vertical distance traveled, y = 4/5 m

Let the speed of cup as it leaves the counter is v and it takes time t to hit the ground.

Use second equation of motion in vertical direction

`y = ut+(1)/(2)at^(2)`

Here acceleration in vertical direction is 9.8 m/s^2.

So,

`(4)/(5) = 0+(1)/(2)*9.8t^(2)`

t = 0.4 second

Now in horizontal direction the acceleration in zero.

Horizontal distance = horizontal velocity x time

x = v t

2 = v (0.4)

v = 5 m/s

Thus, the horizontal velocity of cup as it leaves the counter is 5 m/s.