1.cannon shoots a projectile horizontally (x) at 50 m/s from the top of a 70 m tall cliff. a. How much time does it take the projectile to reach the ground? b. What is the range (dx) of the projectile? am 2. A stunt car traveling toward the edge of a cliff at 25 meters per second lands 50 meters measured horizontally from the edge of the cliff. a) How much time does it take the car to reach the ground? b) Determine the height of the cliff.
Answer (1)
Answer:Here's how to solve these projectile motion problems. Remember that we're ignoring air resistance in these calculations. Problem 1: - Given: - Initial horizontal velocity (v₀ₓ) = 50 m/s- Initial vertical velocity (v₀ᵧ) = 0 m/s (projectile shot horizontally)- Vertical displacement (Δy) = -70 m (negative because it's downward)- Acceleration due to gravity (g) = -9.8 m/s² (negative because it's downward)- a) Time to reach the ground: We can use the following kinematic equation for vertical motion: Δy = v₀ᵧt + (1/2)gt² Plugging in the values: -70 m = (0 m/s)t + (1/2)(-9.8 m/s²)t² Solving for t: t² = 14.29 s²t = √14.29 s² ≈ 3.78 s - b) Range (horizontal distance): The horizontal velocity remains constant since we're ignoring air resistance. The range (dx) is simply: dx = v₀ₓt dx = (50 m/s)(3.78 s) ≈ 189 m Problem 2: - Given: - Initial horizontal velocity (v₀ₓ) = 25 m/s- Horizontal displacement (dx) = 50 m- Acceleration due to gravity (g) = -9.8 m/s²- a) Time to reach the ground: First, find the time using the horizontal motion: dx = v₀ₓt 50 m = (25 m/s)t t = 50 m / 25 m/s = 2 s - b) Height of the cliff: Now use the vertical motion equation, knowing the time: Δy = v₀ᵧt + (1/2)gt² Since the car is traveling horizontally off the cliff, the initial vertical velocity (v₀ᵧ) is 0 m/s. Δy = (0 m/s)(2 s) + (1/2)(-9.8 m/s²)(2 s)² Δy = -19.6 m The height of the cliff is 19.6 m (the negative sign indicates downward displacement). In summary: Problem 1: - a) Time to reach the ground: Approximately 3.78 seconds- b) Range of the projectile: Approximately 189 meters Problem 2: - a) Time to reach the ground: 2 seconds- b) Height of the cliff: 19.6 meters
