To determine the minimum velocity attained by a ball thrown at an angle of 40° with the horizontal, we need to consider the vertical component of the initial velocity. The minimum velocity occurs when the ball reaches its highest point in its trajectory, where the vertical velocity component becomes zero.
Given: Initial velocity (V₀) = 20 m/s Launch angle (θ) = 40°
To find the vertical component of the initial velocity (V₀ₓ) at 40°, we can use trigonometric functions. The vertical component can be calculated as:
V₀ₓ = V₀ * sin(θ)
V₀ₓ = 20 m/s * sin(40°)
V₀ₓ ≈ 20 m/s * 0.6428
V₀ₓ ≈ 12.856 m/s
Therefore, the minimum velocity attained by the ball is approximately 12.856 m/s when it reaches its highest point in the trajectory.