a football is kicke with a velocity of 20 m/s at an angle of 40 degrees with the ground. Find the components. Key: 4 m/s = 1 cm
To find the components of the velocity of the football, we can resolve the velocity into its horizontal and vertical components.
Given:
Initial velocity (V) = 20 m/s
Angle (θ) = 40 degrees
Horizontal Component:
The horizontal component of velocity (Vx) represents the velocity in the x-axis or the ground. To find Vx, we use the formula:
Vx = V * cos(θ)
Vx = 20 m/s * cos(40 degrees)
Vx = 20 m/s * 0.766 (rounding to 3 decimal places)
Vx = 15.32 m/s (rounding to 2 decimal places)
Vertical Component:
The vertical component of velocity (Vy) represents the velocity in the y-axis or perpendicular to the ground. To find Vy, we use the formula:
Vy = V * sin(θ)
Vy = 20 m/s * sin(40 degrees)
Vy = 20 m/s * 0.642 (rounding to 3 decimal places)
Vy = 12.84 m/s (rounding to 2 decimal places)
Therefore, the horizontal component (Vx) of the velocity is 15.32 m/s and the vertical component (Vy) is 12.84 m/s.