Projectile motion beer slide problem

In summary, the conversation discusses finding the initial velocity and direction of a mug that slides off a counter and hits the floor. Various equations and approaches are suggested, including solving for the angle using trigonometric formulas or finding the time it takes for the mug to hit the floor.
  • #1
haydn
27
0

Homework Statement



In a local bar, a customer slides an empty beer mug down the counter for a refill. The bartender is momentarily distracted and does not see the mug, which slides off the counter and strikes the floor 0.60 m from the base of the counter. The height of the counter is 0.900 m.

(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



h=(vi^2*sin^2(x))/(2g)

r=(vi^2*sin(2x))/(g)

the variable x is the angle of the projectile

vi is the initial velocity

The Attempt at a Solution



I thought the angle of the projectile would be 0 since the mug is going straight off the bar but if I plug 0 into the equation I get an answer that doesn't make sense. I also tried -45 but I got an incorrect answer. I think I'll be ok finding the answer if I can figure out the angle...

Thanks
 
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  • #2
I believe there is no initial velocity in the y-direction so only gravity to deal with. In the x-direction you have initial velocity and no gravity to deal with.

y=y0 - 1/2*g*t^2

y=0 when it hits the floor and y0 is the height of the counter, correct.

x=vi*t

vx=vi
vy=-1/2*g*t

Angle=atan(vy/vx)
 
  • #3
haydn said:
h=(vi^2*sin^2(x))/(2g)

r=(vi^2*sin(2x))/(g)

x is the unknown angle of the mug's trajectory as it hits the floor.

There are 2 unknown quantities in these 2 equations, so it can be solved with some algebraic manipulation and knowledge of trig formulas.

An alternative, and equally valid, approach would be to figure out how long it takes the mug to hit the floor.
 
  • #4
Redbelly98 said:
x is the unknown angle of the mug's trajectory as it hits the floor.

There are 2 unknown quantities in these 2 equations, so it can be solved with some algebraic manipulation and knowledge of trig formulas.

An alternative, and equally valid, approach would be to figure out how long it takes the mug to hit the floor.

Alright. I'm having trouble with the algebraic manipulation and I don't think I got the correct answer. Could you solve it and tell me what you get?

Thanks a lot.
 
  • #5
haydn said:
Could you solve it and tell me what you get?

Uh, no, it doesn't work that way here. Sorry!

If you solve each expression for vi^2, you could equate them and then try to find the angle.
 

1. What is projectile motion and how does it relate to the beer slide problem?

Projectile motion is the motion of an object through the air with only the force of gravity acting on it. In the beer slide problem, the can or bottle of beer is considered the projectile as it moves down the slide and the force of gravity causes it to fall towards the ground.

2. What factors affect the projectile motion of the beer slide problem?

The factors that affect the projectile motion of the beer slide problem include the initial speed of the beer, the angle of the slide, and the presence of any external forces such as air resistance or friction.

3. How can we calculate the trajectory of the beer can or bottle in the beer slide problem?

The trajectory of the beer can or bottle in the beer slide problem can be calculated using the equations of projectile motion, taking into account the initial speed, angle of the slide, and any external forces. Alternatively, computer simulations or experiments can also be used to determine the trajectory.

4. Is the beer slide problem a realistic model for projectile motion?

The beer slide problem is a simplified and idealized model for projectile motion. In reality, there may be other factors at play, such as air resistance and the shape of the beer can or bottle, that may affect the motion. However, the beer slide problem is a good illustration of the basic principles of projectile motion.

5. How can understanding projectile motion be useful in real-life situations?

Understanding projectile motion can be useful in a variety of real-life situations, such as in sports (e.g. throwing a ball or shooting a basketball), in engineering and construction (e.g. designing bridges and buildings), and in military operations (e.g. launching missiles). It can also help us understand and predict the motion of objects in everyday situations, such as throwing a frisbee or dropping a pencil from a height.

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