Spring 2001

Part 1.

Given:

• The car is driving at 30 m/s
• The raindrop is falling downward at 40 m/s

Find:

• The movement of the raindrop across the window. (I will use the frame of reference of the raindrop.)

We must realize that there are two vectors, the car’s and the raindrop’s. Then, since they are interacting with the car window these two vectors must be added together. I will draw the vectors from the frame of reference of the rain drop. If you use the reference of the car the movement will be in the other direction.

y y y

30 m/s 30 m/s

-40 m/s 40 m/s

car raindrop both

From the raindrop’s perspective this is the path it traces across the window.

y

We can use the Pythagorean theorem to

solve for the magnitude of R.

30 m/s

R 40 m/s

We also need to find the value of q .

We can solve for it this way.

tan q = 40/30

q = 53 degrees below the horizontal.

Part 2

There are three ropes holding a metal ring stationary. We know what two of the forces are, and we know their components. This is what we have.

y

F_A 35 N

20 N x

F_B

We can use the Pythagorean theorem to find the magnitude of F_A and F_B.

When we add vectors we can actually add the individual x and y components, this will give us the resultant vector.

F_A = 50 N x + 35 N y

+ F_B =-20N x — 10 N y

F_C, the opposite vector, is this: F_C = -30 N x — 25 N y

y

F_B

F_C

Not to scale