Question

A marble rolls with a velocity of 10 mm/s [E] on a game board that is being pulled [60o N of E] at 40.0 mm/s. What is the velocity of the marble relative to the floor?

Answer 1

Answer:

R = 45.82[mm/s], and with an angle of 48.95°

Explanation:

In order to solve this problem, the two vectors will be represented in a scheme, so that an observer located outside the game board will notice that the combined movement is the sum of the moves of the marble and the movement of the board.

In the attached image we can see this sum of vectors. And using the law of the parallelogram we can find the resulting vector, in red color the resulting vector is drawn.

Now decomposing the velocity vector of 40 [mm / s] into the x & y axes.

x = 40*cos(60) = 20 [mm/s]

y = 40*sin(60) = 34.64 [mm/s]

The resultant vector is:

Rx = 20 + 10 = 30 [mm/s]

Ry = 34.64 [mm/s]

Using the pythagorean theorem, we can find the magnitude of the vector

$R = \sqrt{(30)^{2} +(34.64)^{2} }\\ R = \sqrt{2099.92}\\R=45.82[mm/s]$

And the angle with respect to the horizontal can be found using the components calculated above.

tan α = 34.46 / 30

α = 48.95°