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 veloci

Question

Masja

1 month ago

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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 veloci

ty of the marble relative to the floor?

Physics

1 answer:

ValentinkaMS [3.4K] · Answer 1 · 2026-02-27T20:36:59+03:00

Answer:

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

Explanation:

To solve this, the two vectors will be illustrated in a diagram, allowing someone viewing from outside the game board to see that the collective motion comes from both the marble's trajectory and the board's movement.

The image attached displays this vector addition. By utilizing the parallelogram law, we can derive the resultant vector, shown in red.

Next, we will break down the velocity vector of 40 [mm/s] into its x and y components.

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

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

<pConsequently, the resultant vector is:

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

Ry = 34.64 [mm/s]

<pApplying the Pythagorean theorem, we can ascertain the vector’s magnitude

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

Next, we can calculate the angle relative to the horizontal using the previously obtained components.

tan α = 34.46 / 30

α = 48.95°