Question

1. Projectile Motion There is a 10 m vertical cliff next to the ocean, but the top of it is not flat. Instead it slopes upward away from the edge at 30° above the horizontal. At the top of that hill, someone loses their traction, slides down, and then slides off the edge of the cliff, into the air at a speed of 3 m/s. Where will they land in the water below?​

Answer 1

To determine where the person will land in the water below, we need to analyze the projectile motion of their slide down the cliff.

1. Split the motion into horizontal and vertical components:

- The horizontal motion is unaffected by gravity and continues at a constant velocity of 3 m/s.

- The vertical motion is affected by gravity and follows a parabolic trajectory.

2. Calculate the time of flight:

- Since the initial vertical velocity is zero (the person loses traction and slides down), the time taken to reach the maximum height can be found using the equation: v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time taken.

- In this case, the final velocity is 0 m/s (at the highest point of the trajectory), the initial velocity is 0 m/s (person loses traction and starts sliding downward), and the acceleration due to gravity is -9.8 m/s^2 (assuming downward as negative).

- Solving for t, we get t = 0 - 0 / -9.8 = 0 seconds.

- This means that the person reaches the maximum height instantly and begins to descend.

3. Calculate the horizontal distance traveled:

- The horizontal distance can be calculated using the equation: distance = velocity × time.

- In this case, the horizontal velocity is 3 m/s (given) and the time of flight is 0 seconds (as calculated above).

- Therefore, the horizontal distance traveled is 3 m/s × 0 s = 0 meters.

4. Determine the vertical distance fallen:

- To find the vertical distance fallen, we need to calculate the time taken to reach the water below.

- The vertical distance fallen can be calculated using the equation: distance = u × t + (1/2) × a × t^2, where u is the initial vertical velocity, t is the time taken, and a is the acceleration due to gravity.

- In this case, the initial vertical velocity is 0 m/s, the time taken is the same as the time of flight (0 seconds), and the acceleration due to gravity is -9.8 m/s^2.

- Solving for distance, we get distance = 0 × 0 + (1/2) × (-9.8) × (0^2) = 0 meters.

- This means that the person falls vertically by 0 meters.

Based on the calculations, the person will land directly below the edge of the cliff, at a horizontal distance of 0 meters and a vertical distance of 0 meters from the cliff.

Step-by-step explanation: