If an average net force of 20N at 45* is applied to a 0.35 kg water balloon for 0.12s. how far away should the catcher stand? Assume release height and cathc height are the same and air resistance is not a factor.
0.5
To determine the distance the catcher should stand in order to catch the water balloon, we need to analyze the motion of the balloon using Newton's second law of motion.
1. First, let's determine the acceleration of the water balloon:
- Newton's second law states that force (F) is equal to mass (m) multiplied by acceleration (a): F = m * a.
- In our case, the net force acting on the balloon is 20 N at an angle of 45 degrees.
- The net force acting on an object can be calculated by resolving it into its horizontal and vertical components. The vertical component is responsible for the acceleration.
- Since the force is at an angle of 45 degrees, we can find its vertical component (Fy) using trigonometry: Fy = F * sin(45).
- Substitute the given value: Fy = 20 N * sin(45) ≈ 14.14 N.
- Now we can calculate the acceleration using the formula: F = m * a.
- Substitute the known values: 14.14 N = 0.35 kg * a.
- Solving for a, we find that the acceleration is approximately 40.4 m/s^2.
2. Next, let's find the velocity of the water balloon:
- The acceleration of the balloon is constant, so we can use the kinematic equation: v = u + a * t.
- Since the initial velocity (u) of the balloon is assumed to be zero (at rest before release): v = 0 + 40.4 m/s^2 * 0.12 s.
- The velocity of the balloon is approximately 4.85 m/s.
3. Now, let's calculate the distance the balloon should travel:
- The distance traveled by the balloon can be determined using the kinematic equation: s = u * t + 0.5 * a * t^2.
- Since the initial velocity (u) is zero: s = 0 * 0.12 s + 0.5 * 40.4 m/s^2 * (0.12 s)^2.
- Simplifying the equation: s = 0 + 0.5 * 40.4 m/s^2 * 0.0144 s^2.
- The distance traveled by the balloon is approximately 0.2918 meters (or 29.18 centimeters).
Therefore, the catcher should stand approximately 29.18 centimeters away from the point where the water balloon is released in order to catch it.