What is the velocity of raindrops in relation to the Earth and a car?

[EBBAzores]

Homework Statement

A car travels to east with 50 km/h. It's rainning vertically in relation to the Earth. The raindrops on the lateral windows of the car make a 60 degree angle with the vertical. Determine the velocity of the raindrops in relation to:
a) The Earth
b) The car

Homework Equations

I really don't know what to do here xD

The Attempt at a Solution

I really don't know what to do here xD

 

[TSny]

Hi. This is a relative velocity problem. I'll try to get you started.

Take toward the right on a sheet of paper to represent east and toward the top of the paper as representing vertically upward from the earth.

Draw a vector representing the velocity vector of the car relative to the earth:$\vec{V}$_C/E
Draw a vector representing the velocity of the rain relative to the earth: $\vec{V}$_R/E
Draw a vector representing the velocity of the rain relative to the car: $\vec{V}$_R/C

Which two of these vectors when added together will equal the third vector?

 

[EBBAzores]

V_C/E plus V_R/E? That's equal to the 3rd vector

 

[SammyS]

V_C/E plus V_R/E? That's equal to the 3rd vector

No.

How are $\displaystyle \vec{v}_{C/E}\,,\ \vec{v}_{R/E}\,,\text{ and }\vec{v}_{R/C}$ related?

 

[EBBAzores]

V_r/c = V_c/e + V_r/e

so by that logic V_r/c = 50/sin(60)

and of course V_r/e = V_r/c cos(60) = (50cos(60))/sin(60)

and that's the answer by this logic right?

 

[TSny]

V_r/c = V_c/e + V_r/e

This is not the correct relation between the vectors. Did you draw the three vectors? If you add V_c/e + V_r/e graphically, you will see that the result does not point in the direction that you would expect for v_r/c.

Can you see the correct relationship?

so by that logic V_r/c = 50/sin(60)

and of course V_r/e = V_r/c cos(60) = (50cos(60))/sin(60)

and that's the answer by this logic right?

When you construct the correct velocity diagram, see if you still get these answers.

 

[EBBAzores]

So from what I draw I understood that the actual velocity diagram is given by V_c/e = V_r/e + V_r/c but besides that the results that I obtained before were right

 

[TSny]

So from what I draw I understood that the actual velocity diagram is given by V_c/e = V_r/e + V_r/c but besides that the results that I obtained before were right

Let's see.

V_r/e = velocity of rain with respect to the Earth which is a vector pointing straight down.

V_r/c = velocity of rain with respect to the car which is a vector pointing down and to the left (i.e., down and toward the west).

If I place these vectors "head-to-tail" to add them, I get a resultant vector that points down and to the left (but more steeply downward than V_r/c).

This doesn't agree with V_c/e which is the velocity of the car with respect to the Earth and points horizontally toward the right.

 

[EBBAzores]

So the V_r/e + V_c/e = V_r/c

 

[TSny]

There's a general rule for setting up correct relative velocity equations. Suppose you have three objects a, b, and c which move relatively to one another. A correct equation would be

V_a/c = V_a/b + V_b/c

Another correct relation would be

V_b/a = V_b/c + V_c/a

The general rule is that whatever subscript appears first on the left side of the equation is also the first subscript on the right side of the equation. The last subscript on the left side is also the last subscript on the right side. Whatever subscript does not appear on the left side will appear on the right as "sandwiched between" the first and last subscripts.

Thus in the first equation above, "a" appears first on both sides of the equation and "c" appears last on both sides. "b" is sandwiched between "a" and "c" on the right side.

See if this can help you set up a correct equation for the velocities in your problem.

 

[TSny]

Another rule that is often useful is V_a/b = -V_b/a. (You might not need this rule to solve the particular problem you are working on now, but it might come in handy in other problems.)

Example, if a car is moving toward the east at 50 mph relative to the earth, then the Earth would be moving at 50 mph toward the west relative to the car: V_c/e = -V_e/c

 

[EBBAzores]

V_r/e=V_r/c + V_c/e...

Seriously I'm feeling so stupid right I have an exam in 3h hours and I'm feeling like a don't know a thing!

 

[EBBAzores]

Either way thanks for the help you've been given me

 

[TSny]

V_r/e=V_r/c + V_c/e...

Seriously I'm feeling so stupid right I have an exam in 3h hours and I'm feeling like a don't know a thing!

That's the correct equation. Draw a velocity diagram representing this equation and you'll be able to use trig to get the answer. (The answers for the magnitudes of the velocities will agree with what you got before.)

Good luck with your exam.

 

[azizlwl]

I guess the raindrops must be at terminal velocity.