Estimating speed and angle of raindrops

I encountered 2 truly challenging problems (very challenging to me) and I hope someone can help me...any help is truly appreciated!

1) While driving north at 25m/s during a rainstrom you observe that the rain makes an angle of 38 degrees with the vertical. While driving back home moments later at the same speed but in the opposite direction, you see that the rain is falling straight down. From theses observations, determine the speed and angle of the raindrops relative to the ground.

[I know this is a realtive velocity problem so I should use the realtive velocity formula V(ac)=V(ab)+V(bc), but the speed of the raindrops aren't given...then how can I calculate? I am really stuck now...can someone kindly help me?]

2) A ball with mass m is placed against the inner edge of a cylinder at a height of 4r where r is the radius of the cylinder. What initial horizontal speed v tangential to the cylinder wall should be given to the ball so that it will complete 2 revolutions around the inside of the cylinder before it hits the ground? Ignore friction and express the answer in terms of the variables given in the question.
[the ball is not really following a circular motion, it will never get back to the same point, so would the radius still be r? I am really puzzled by this question...]

Thanks a lot!

 

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Rain falls.

 

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Rain kills as it falls. Lie in the rain long enough and your skin will be punctured with holes

 

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not enough info...

 

Each raindrop has a velocity with 2 components, Vx and Vy, and you have are going north or south with a velocity v0.
When you go south, the relative velocity of the rain wrt you is 0, so that its x component is equal to your velocity, i.e. Vx = v0.
When you go north, the x component of the relative velocity becomes Vx + v0 = 2v0. The y component is Vy downward. So that the angle of the rain relative to you is tan(α ) = 2v0/Vy from which you get Vy = 2v0/tan(α ) , which is Vy = 64 m/sec.
Now that you have Vx and Vy you can calculate the total velocity of the rain and the angle

 

Good one!

"2) A ball with mass m is placed against the inner edge of a cylinder at a height of 4r where r is the radius of the cylinder. What initial horizontal speed v tangential to the cylinder wall should be given to the ball so that it will complete 2 revolutions around the inside of the cylinder before it hits the ground? Ignore friction and express the answer in terms of the variables given in the question."

OK what I'm seeing is that the wicked teacher

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is looking for an equation, not a number, remember that as we go. what you are being asked to do is combine polar coordinates with a vertical coordinate to analyze this clever little three-D scenario.

You know how long it takes the ball to fall that distance, and you are to ignore friction so you can go with that time. During that time, the ball is rolling around on the inside of the pipe . . . I assume you have some equations of motion in polar coordinates at hand? Turn the algebra crank and give the wicked teacher a pretty equation and draw a box around it so the wicked teacher can find it.

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Thanks spacester & 1100f for helping me!

 

This is a really terrible, tough problem...:bugeye:

I have a couple of questions:
Will the ball be in UNIFORM circular motion???

The ball circles down to the bottom, so the circular path is definitely tilted...then in what direction will the centripetal force point??? I don't think it will point horizontally...

 

Thanks a lot!

But what if the question is modified so that "While driving back home moments later at the same speed but in the opposite direction, you see that the rain is falling at an angle of 20 degrees to the vertical" instead of vertically falling? How can I solve this problem?

 

please tell me are u dumping ur physics HW here? Have u actually thought out each problem beforehand? not to offend you, just asking.

 

If he does, I reasonbly sure he is lying.

I want to give his teacher an "A" for the exam. I alway tried to make at least half of the questions on mine such that no formulae memorized from the book (or written inside your shirt cuff, etc.) was useful without thought / understanding.

When exam time comes, the "help" he got here, instead of thinking for himself, will be "rewarded" - Keep up the good work "teach."

 

OK, I'm not going to give this away, I get the point expressed by others, but I've a mind to help you out, I hope that's OK.

Now, I did already gave you a lot, and I didn't get much feedback on how things went when you tried what I suggested. So I'll wait for your next post.

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I got an answer of v = [pi*sqrt(2rg)] m/s, but I don't totally understand the question.

My major confuse comes from the following 2 questions:

I am not sure will the ball be in UNIFORM circular motion in such cases??? (not completing the CIRCLE...) or is it NON-uniform circular motion?

The ball circles down to the bottom, so the circular path is definitely tilted...then in what direction will the centripetal force point??? I don't think it will point horizontally...but if not, at what angle will it point?

Thanks!

 

What course is this? Mathematics, Dynamics, Physics? High School? College?

I'm thinking that you don't need to worry about forces and angles. Just treat the path of motion as circular, that's the "ignore friction" part.

I'm not thrilled with the assumptions made by this problem.

 

Physics, first year university...

 

Well, if you want a description of the path, split it into components. What's happening in the horizontal plane and in the vertical direction? Why is this bothering you, anyway?

Hint: what do you remember about normal forces?

How's it going?

 

It's bothering me because I am sure the ball will not following a circular path as it circles down to the bottom...and also the speed will certainly be higher at the bottom than the top and UNIFORM circular motion requires uniform speed, right?

perpendicular to contact surfaces...so maybe the centripetal force is still horizontal...but I think gravity is messing things up in this question...is it?

So so...my prof make it so calculus-based but I haven't learnt much calculus in high school...the mathemtatics is simply beyond my level of understanding...and the notations are all different so I am forced to learn physics in a completely different way than I was in high school...

 

Hi kingwinner,
For the ball in cylinder problem, the horizontal component is circular and uniform. If you viewed it from above, it would follow a circle at constant speed.
The vertical motion is constant acceleration due to gravity.

 

You'll definitely want to get your calculus up to scratch if you're planning on doing physics much further - I'd recommend taking calculus or mathematical methods courses if you can - you probably won't enjoy them, but once you can do the maths, you'll find it a lot easier to learn the physics. Do you know what area of physics you want to aim for?

 

Why can we just view it from above? Is it because the vertical component and horizontal component are inpendent? (i.e. gravity only affacts the vertical component?)