I had ask this question of you before but I didn't understand your response. Can you please clearify further. The question is:
a skateboarder moving at v = 5 m/s along a horizontal section of a track that is slanted upward by 48° above the horizontal at its end, which is h = 0.52 m above the ground. When she leaves the track, she follows the characteristic path of projectile motion. Ignoring friction and air resistance, find the maximum height H to which she rises above the end of the track.
To find the maximum height H to which the skateboarder rises above the end of the track, we can analyze the problem using the principles of projectile motion. Here's how you could approach it:
1. Break down the skateboarder's initial velocity into horizontal and vertical components: For a skateboarder moving at speed v = 5 m/s, the horizontal component of velocity (v_x) remains constant throughout, while the vertical component (v_y) changes due to gravity. Since the track is slanted upward by 48°, we need to find v_x and v_y.
- Horizontal component (v_x): Since the skateboarder is moving horizontally along the track, there is no change in velocity in the horizontal direction. Therefore, v_x remains at 5 m/s.
- Vertical component (v_y): To find v_y, we can use trigonometry. The angle formed between the horizontal and the track is 48°. Therefore, v_y can be calculated as v * sin(48°).
2. Determine the time of flight: To find the maximum height, we need to know the time it takes for the skateboarder to reach the highest point. Using the equation for vertical motion:
- Let's denote the time of flight as t.
- The equation for vertical displacement is given by: H = v_y * t - (1/2) * g * t^2, where g is the acceleration due to gravity (approximately 9.8 m/s^2).
- At the highest point, the vertical velocity becomes zero, so v_y - g * t = 0.
Solving the equation v_y - g * t = 0 for t will give us the time of flight.
3. Calculate the maximum height (H): Once we have the time of flight, we can substitute it back into the equation for vertical displacement.
- The equation for vertical displacement becomes: H = v_y * t - (1/2) * g * t^2.
By substituting the values of v_y and t, we can find the maximum height H.
Therefore, by following these steps, you can calculate the maximum height H to which the skateboarder rises above the end of the track.