Question

A football was kicked with an initial velocity of 40m/s at an angle of 35 degrees with the horizontal. What are the horizontal and vertical commponents of the initial velocity?

Answer 1

To calculate the horizontal and vertical components of the football's initial velocity, one uses the cosine and sine functions respectively, resulting in a horizontal component of approximately 32.8 m/s and a vertical component of approximately 22.9 m/s.

Step-by-step explanation:

The student is dealing with a problem that requires the use of trigonometry to decompose the initial velocity of a football into its horizontal and vertical components. The initial velocity is given as 40 m/s at an angle of 35 degrees with the horizontal.

To find the horizontal component (Vx), we use the cosine function:

• Vx = V * cos(θ)

To find the vertical component (Vy), we use the sine function:

• Vy = V * sin(θ)

Where V is the initial velocity and θ is the launch angle. Plugging the values in, we get:

Vx = 40 m/s * cos(35°) = 32.8 m/s (2 d.p.)

Vy = 40 m/s * sin(35°) = 22.9 m/s (2 d.p.)

Thus, the horizontal component of the velocity is approximately 32.8 m/s, and the vertical component is approximately 22.9 m/s.