To determine the distance at which the stone will hit the ground after the rope breaks, we can analyze the motion of the stone as it follows a horizontal parabolic trajectory. Here's how you can approach this problem step by step:
1. Calculate the initial velocity (V₀) of the stone:
- Given that the rope is 1 meter long and the stone is rotating at 240 rpm, convert the rpm to rad/s (revolutions per minute to radians per second).
- The velocity of an object in circular motion can be calculated using the formula: v = ωr, where ω is the angular velocity in rad/s and r is the radius of the circle (length of the rope in this case).
2. Determine the time it takes for the stone to fall:
- Since the stone is moving horizontally, the time it takes to fall can be calculated using the formula: t = √(2h/g), where h is the height (3.6 m) and g is the acceleration due to gravity (9.81 m/s²).
3. Find the horizontal distance the stone travels during this time:
- The horizontal distance can be calculated as: d = V₀ * t, where V₀ is the initial velocity calculated in step 1 and t is the time calculated in step 2.
4. The stone will hit the ground at this horizontal distance from the point where the rope broke. This distance can be determined by considering the horizontal distance calculated in step 3.
By following these steps and performing the calculations, you can find the distance at which the stone will hit the ground after the rope breaks in the scenario described. Remember to consider the assumptions made in the problem, such as the stone following a parabolic trajectory and neglecting air resistance.
