You lose your footing and slide of of your roof. Fortunately, you have placed a safety net whose center is positioned at a horizontal distance of 4.15m, measured from a point directly below the edge of the roof- and indeed you land in the center of the net. If the roof slopes downward at a 26 degree angle below horizontal, and your speed as you leave the roof is 3.70m/s, high is the edge of the roof above the level of the safety net?

Question

You lose your footing and slide of of your roof. Fortunately, you have placed a safety net whose center is positioned at a horizontal distance of 4.15m, measured from a point directly below the edge of the roof- and indeed you land in the center of the net. If the roof slopes downward at a 26 degree angle below horizontal, and your speed as you leave the roof is 3.70m/s, high is the edge of the roof above the level of the safety net?

Answer 1

To find the height of the edge of the roof above the level of the safety net, we can use trigonometry and the concept of projectile motion.

Here's the step-by-step process:

1. Draw a diagram: Sketch a diagram of the situation to better visualize the problem. Label the relevant quantities such as the distance from the edge of the roof to the center of the net (4.15m) and the slope angle (26 degrees).

2. Decompose the velocity: Since the motion is two-dimensional, we need to analyze the horizontal and vertical components separately. The horizontal component of the velocity remains constant, while the vertical component changes due to gravity.

- Horizontal component (Vx): Given the initial speed (3.70 m/s), we can find the horizontal component using the equation Vx = V * cos(theta), where theta is the angle of the slope (26 degrees).
- Vertical component (Vy): Similarly, V * sin(theta) gives us the vertical component.

3. Calculate the time of flight: The total time of flight is the time taken for you to reach the center of the net. We can calculate it using the formula t = d / Vx, where d is the horizontal distance to the net (4.15m).

4. Determine the vertical displacement: Using the equation of motion in the vertical direction, we can find the displacement of the object. The equation is given by Δy = Vyt - 0.5 * g * t^2, where g is the acceleration due to gravity (approximately 9.8 m/s^2).

5. Calculate the height: The height of the edge of the roof above the level of the safety net is equal to the vertical displacement. Subtracting this value from the center of the net will give us the desired height.

Following this process, you should be able to determine the height of the edge of the roof above the level of the safety net.