A baseball player hits the ball at a speed of 20.1 m/s and an angle of 30 degrees. What is the baseball's horizontal velocity?

What is the baseball's vertical velocity?

How long does it take the baseball to get 28m in front of home plate?

To find the baseball's horizontal velocity, you need to determine the component of the initial velocity in the horizontal direction. The horizontal velocity remains constant throughout the motion since there are no horizontal forces acting on the baseball.

The horizontal component of the initial velocity can be found using the formula: Vx = V * cos(theta), where V is the magnitude of the initial velocity and theta is the launch angle.

In this case, the magnitude of the initial velocity (V) is given as 20.1 m/s, and the launch angle (theta) is given as 30 degrees. Plugging in these values into the formula, we get:

Vx = 20.1 m/s * cos(30°)
= 20.1 m/s * 0.866
≈ 17.39 m/s

Therefore, the baseball's horizontal velocity is approximately 17.39 m/s. This means that the baseball is moving horizontally at a constant speed of 17.39 m/s.

Next, let's find the baseball's vertical velocity. The vertical component of the initial velocity can be found using the formula: Vy = V * sin(theta), similar to the horizontal velocity calculation.

Using the same values for V and theta, we have:

Vy = 20.1 m/s * sin(30°)
= 20.1 m/s * 0.5
= 10.05 m/s

Therefore, the baseball's vertical velocity is 10.05 m/s. This means that the baseball is initially moving vertically at 10.05 m/s, but due to the acceleration due to gravity, it will decrease until it reaches its maximum height and eventually falls back down.

Lastly, to find the time it takes for the baseball to travel 28 m in front of home plate, we need to consider only the horizontal motion because the vertical motion does not affect the horizontal displacement.

To find the time, we can use the equation: d = Vx * t, where d is the horizontal displacement and Vx is the horizontal velocity. Rearranging the equation, we have:

t = d / Vx

Plugging in the values, with a displacement of 28 m and horizontal velocity of 17.39 m/s, we get:

t = 28 m / 17.39 m/s
≈ 1.61 seconds

Therefore, it takes approximately 1.61 seconds for the baseball to travel 28 m in front of home plate.