To write the initial velocity vector of the ball V in component form, we need to break it down into its horizontal and vertical components.
Given:
Initial velocity of the ball V = 60 mph
Upward angle of 30°
To find the horizontal component, we need to find the velocity of the ball in the horizontal direction. This can be found using the formula:
Horizontal component = Initial velocity * cos(angle)
In this case, the initial velocity is 60 mph and the angle is 30°. So, we can calculate the horizontal component as follows:
Horizontal component = 60 mph * cos(30°)
To find the vertical component, we need to find the velocity of the ball in the vertical direction. This can be found using the formula:
Vertical component = Initial velocity * sin(angle)
In this case, the initial velocity is 60 mph and the angle is 30°. So, we can calculate the vertical component as follows:
Vertical component = 60 mph * sin(30°)
Therefore, the initial velocity vector of the ball V in component form is:
V = (Horizontal component, Vertical component)
Now, let's calculate the values:
Horizontal component = 60 mph * cos(30°) = 60 * 0.866 = 51.96 mph
Vertical component = 60 mph * sin(30°) = 60 * 0.5 = 30 mph
So, the initial velocity vector V is:
V = (51.96 mph, 30 mph)