a softball is thrown at a speed of 40 miles per hour in a course that makes an angle of 60 degrees with the positive x axis. what is the initial speed in the horizontal direction?
Xo = 40*Cos60 = 20 mi/h.
To determine the initial speed in the horizontal direction, we need to find the horizontal component of the velocity of the softball.
Given:
- Speed of the softball = 40 miles per hour
- Angle with the positive x-axis = 60 degrees
To calculate the horizontal component, use the formula:
Horizontal component = Speed * cos(angle)
First, convert the speed from miles per hour to a consistent unit such as meters per second (m/s):
1 mile = 1609.34 meters (approximately)
1 hour = 3600 seconds
So, 40 miles per hour = 40 * 1609.34 / 3600 ≈ 17.94 m/s
Now, calculate the horizontal component:
Horizontal component = 17.94 m/s * cos(60 degrees)
The cosine of 60 degrees is 0.5, so:
Horizontal component = 17.94 m/s * 0.5
Horizontal component ≈ 8.97 m/s
Therefore, the initial speed in the horizontal direction is approximately 8.97 meters per second.