Question

an outfielder throws a baseball to the first baseman at a speed of 19.6 meters per second and an angle of 30 above the horizontal. Calculate the horizontal and vertical components of the baseball’s initial velocity.

Answer 1

The horizontal component of the baseball's initial velocity is approximately 16.97 m/s, and the vertical component is 9.8 m/s, calculated using trigonometric functions with the given speed and angle of 19.6 m/s and 30 degrees respectively.

Step-by-step explanation:

To calculate the horizontal and vertical components of a baseball's initial velocity thrown at a speed of 19.6 meters per second with an angle of 30 degrees above the horizontal, we can use trigonometric functions: cosine to find the horizontal component (Vx) and sine to find the vertical component (Vy).

The horizontal component of velocity (Vx) is determined by the following formula:

• Vx = V * cos(θ)

Where V is the initial velocity and θ is the angle of throw.

The vertical component of velocity (Vy) is given by:

• Vy = V * sin(θ)

Let's apply these to the given problem:

• Vx = 19.6 m/s * cos(30°)
• Vy = 19.6 m/s * sin(30°)

Calculating these components provides us with:

• Vx = 19.6 m/s * (\(√3\)/2) ≈ 16.97 m/s
• Vy = 19.6 m/s * (1/2) = 9.8 m/s

The horizontal component is approximately 16.97 m/s, and the vertical component is 9.8 m/s.