What is the initial velocity of Austin as he kicks a soccer ball at an angle of 35.0° with an initial velocity of 18.0 m/s?
The horizontal and vertical components of the initial velocity can be calculated as follows:
- Horizontal component (Vx) = 14.74 m/s
- Vertical component (Vy) = 10.32 m/s
Calculation of Horizontal and Vertical Components of Initial Velocity
Horizontal Component:
The horizontal component of the initial velocity (Vx) can be calculated using the formula Vx = Vcos∅, where V is the initial velocity and ∅ is the angle to the horizontal. From the given data:
V = 18.0 m/s,
∅ = 35.0°.
Substitute the values into the formula:
Vx = 18(cos35.0°)
Vx = 18(0.819)
Vx ≈ 14.74 m/s.
Therefore, the horizontal component of the initial velocity is approximately 14.74 m/s.
Vertical Component:
The vertical component of the initial velocity (Vy) can be calculated using the formula Vy = Vsin∅. Substitute the given values into the formula:
Vy = 18(sin35°)
Vy ≈ 10.32 m/s.
Hence, the vertical component of the initial velocity is approximately 10.32 m/s.
In summary, Austin kicks a soccer ball with a horizontal component of 14.74 m/s and a vertical component of 10.32 m/s at an angle of 35.0° with an initial velocity of 18.0 m/s.