To find the greatest possible range of the ball when air resistance is negligible, we can use the kinematic equations of motion.
The horizontal and vertical motions are independent of each other, so we can analyze them separately.
Vertical Motion: The initial vertical velocity (Vy) can be calculated using the initial velocity (V) and the launch angle (θ). Since the angle is 45 degrees, and the initial velocity is 40 m/s, we can use trigonometry to find Vy:
Vy = V * sin(θ) = 40 m/s * sin(45°) ≈ 28.28 m/s
The time of flight (T) can be determined using the vertical motion equation:
T = 2 * Vy / g
where g is the acceleration due to gravity (approximately 9.8 m/s²).
T = 2 * 28.28 m/s / 9.8 m/s² ≈ 5.78 s
Horizontal Motion: The horizontal velocity (Vx) remains constant throughout the motion. It can be calculated using the initial velocity (V) and the launch angle (θ):
Vx = V * cos(θ) = 40 m/s * cos(45°) ≈ 28.28 m/s
To find the range (R), we can use the equation:
R = Vx * T ≈ 28.28 m/s * 5.78 s ≈ 163.5 m
Therefore, the greatest possible range of the ball when air resistance is considered to be negligible is approximately 163.5 meters.