Question

Matt is trying his hardest to beat his best friend at mario party. in the game, mario is walking forward but a conveyor belt is moving him to the right at the same time. To matt, it looks like mario is traveling 6 m/s at an angle of 23 degrees above the x-axis. How fast is the conveyor belt and how fast is mario?

Answer 1

Mario's speed and the conveyor belt's speed can be determined using vector decomposition, by breaking down Mario's net velocity into horizontal and vertical components using trigonometric functions.

Step-by-step explanation:

Matt is observing Mario's net velocity as he is walking forward on a moving conveyor belt. To solve for Mario's walking speed and the speed of the conveyor belt separately, we can use vector decomposition. The net velocity given is 6 m/s at an angle of 23 degrees above the x-axis. This can be represented as a vector and broken down into two components: one in the horizontal direction, representing the conveyor belt's speed, and one in the vertical direction, representing Mario's walking speed relative to the conveyor belt.

Step-by-step solution:

1. Use trigonometry to resolve the given vector into horizontal (x) and vertical (y) components.
2. The horizontal component Vx is found using the cosine function: Vx = Vnet * cos(θ), where Vnet = 6 m/s and θ = 23°.
3. The vertical component Vy is found using the sine function: Vy = Vnet * sin(θ).
4. Calculate the values: Vx = 6 * cos(23°) and Vy = 6 * sin(23°).
5. The horizontal component Vx represents the speed of the conveyor belt, and the vertical component Vy represents Mario's walking speed.

Therefore, Mario's speed is the vertical component, and the conveyor belt's speed is the horizontal component.