Question

A major leaguer hits a baseball so that it leaves the bat at a speed of 30.8 m/s and at an angle of 34.7° above the horizontal. What is the initial vertical velocity of the baseball?

Answer 1

The initial vertical velocity of the baseball is approximately 17.6 m/s, which is calculated using the vertical component of the total velocity and the angle of release.

Step-by-step explanation:

To find the initial vertical velocity of the baseball, we use the component of the total velocity in the vertical direction. Given the baseball leaves the bat at a speed of 30.8 m/s and at an angle of 34.7° above the horizontal, we can use the sine function to calculate this vertical component:

Vertical Velocity = Total Velocity × sin(Angle)

We have:

• Total Velocity (v) = 30.8 m/s
• Angle (θ) = 34.7°

So, the calculation is:

Vertical Velocity = 30.8 m/s × sin(34.7°)

Using a calculator to find the sine of 34.7° and multiplying by 30.8 m/s, the initial vertical velocity of the baseball is:

Vertical Velocity = 30.8 m/s × 0.571 (sine of 34.7°)

Vertical Velocity ≈ 17.6 m/s