Falling coffee mug, time of descent

In summary, the customer accidentally slides an empty coffee mug off the counter, causing it to fall 1.9m from the base of the counter. The employee is momentarily distracted and does not see the mug. The height of the counter is .840m. To find the velocity of the mug, the kinematic equations can be used. By determining the time it takes for the mug to fall in the x-direction and using that in an equation relating distance, time, and initial velocity in the y-direction, you can find the initial velocity of the mug. Additionally, the final velocity in the y-direction can be found to determine the angle of the mug just before it hits the floor.
  • #1
chocolatelover
239
0

Homework Statement



A customer slides an empty coffee mug down the counter. The employee is momentarily distracted and does not see the mug, which slides off the counter and strikes the floor 1.9m from the base of the counter. The height of the counter is .840m.
a. With what velocity did the mug leave the counter?
b. What was the direction of the mug's velocity just before it hit the floor?

Homework Equations





The Attempt at a Solution



a. I'm not sure how to find the velocity. Would I use one of the kinematic equations?


b. Theta=tan-1(.840/1.9)
=23.85

360-23.85=336 below the horizontal axis

Thank you very much
 
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  • #2
You have two situations, one in the x-direction, and one in the y-direction. Figure out the time it takes the coffee mug to fall x metres in the x-direction. You can then plug that time into an equation relating the distance traveled in the y-direction, the time, and the initial velocity in the y-direction. From this you can get the initial velocity of the mug. You can also get the final velocity in the y-direction of the mug, and then find your angle that way.
 
  • #3
Thank you very much

Would I use this equation?

xf=vxi+1/2axt

(Figure out the time it takes the coffee mug to fall x metres in the x-direction) Would I use one of the kinematic equations?

I'm looking for the final velocity, right?

Thank you
 
Last edited:
  • #4
What would be your a then? Do you have an acceleration in the x-direction? Last time I checked, gravity worked down towards the centre of the earth. ;)
 

1. How does the time of descent of a falling coffee mug change with different heights?

The time of descent of a falling coffee mug is directly proportional to the height from which it is dropped. This means that the higher the mug is dropped from, the longer it will take to reach the ground.

2. Does the shape or weight of the coffee mug affect its time of descent?

Yes, both the shape and weight of the coffee mug can affect its time of descent. A heavier mug will experience a greater force of gravity and therefore fall faster. Additionally, a mug with a sleeker, more aerodynamic shape will experience less air resistance and fall faster than a mug with a bulkier shape.

3. Is there a limit to how fast a coffee mug can fall?

Yes, there is a limit to how fast a coffee mug can fall. This is known as terminal velocity, which occurs when the force of gravity is equal to the force of air resistance. At this point, the mug will no longer accelerate and will fall at a constant speed.

4. Can the time of descent be affected by external factors?

Yes, the time of descent can be affected by external factors such as air resistance, wind, and surface conditions. These factors can alter the mug's velocity and therefore affect its time of descent.

5. Can the time of descent be calculated using a mathematical formula?

Yes, the time of descent can be calculated using the equation t = √(2h/g), where t is the time of descent, h is the height from which the mug is dropped, and g is the acceleration due to gravity. However, this formula assumes no air resistance and a constant gravitational force, so the actual time of descent may vary slightly from the calculated value.

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