To find the separation between the poles, we need to determine the horizontal distance covered by the ball while clearing the poles.
Let's analyze the motion of the ball. The initial velocity of the ball is given as 7√2 m/s at an angle of 45° with the horizontal. We can break down this initial velocity into horizontal and vertical components.
The horizontal component of the velocity remains constant throughout the motion. It can be calculated as:
Horizontal component = Initial velocity * cos(angle)
Horizontal component = 7√2 m/s * cos(45°) = 7 m/s
The vertical component of the velocity is responsible for the motion of the ball in the vertical direction. It is affected by gravity and follows a projectile motion trajectory. We can analyze the vertical motion to determine the time of flight.
The maximum height reached by the ball can be calculated using the formula:
Maximum height = (Initial vertical velocity)^2 / (2 * acceleration due to gravity)
Maximum height = (7√2 m/s * sin(45°))^2 / (2 * 9.8 m/s²) = 5.24 m
Since the poles are each 90 cm in height, the total clearance required is 2 * 0.9 m = 1.8 m.
Using the equation for vertical displacement in projectile motion:
Vertical displacement = (Initial vertical velocity)^2 * sin^2(angle) / (2 * acceleration due to gravity)
1.8 m = (7√2 m/s * sin(45°))^2 * sin^2(45°) / (2 * 9.8 m/s²)
Simplifying this equation will give us the time of flight.
From the time of flight, we can then calculate the horizontal distance covered using the equation:
Horizontal distance = Horizontal component * time of flight
With the final value of the horizontal distance, we can determine the separation between the poles.