An outfielder throws to the second baseman, a distance of 120ft at a 20degree angle. Whats the min velocity he has to throw the ball to get it to the base?

To find the minimum velocity the outfielder needs to throw the ball to reach the second baseman at a distance of 120 feet and an angle of 20 degrees, we can use the kinematic equations of projectile motion. Specifically, we'll use the equation for the vertical component of velocity:

v_vertical = v_initial * sin(angle)

where v_vertical is the vertical component of velocity, v_initial is the initial velocity, and angle is the launch angle.

Since we want to find the minimum velocity, we know that the ball will follow a parabolic trajectory, reaching its highest point at the midway distance of the throw. At this point, the vertical component of velocity will be zero. Therefore, we can find the initial velocity at this point and use it to determine the minimum velocity.

Using the equation for horizontal motion:

distance = v_horizontal * time

we know that at the midpoint, the distance traveled horizontally will be half of the total distance:

distance = 1/2 * 120ft = 60ft

Now, let's find the time it takes for the ball to reach the midpoint. Since the vertical motion is symmetric, the time taken to reach the highest point will be half the total time of flight:

time_to_midpoint = time_of_flight / 2

Next, we can use the equation for vertical motion to relate time and initial velocity:

0 = v_initial * sin(angle) - g * time_to_midpoint

where g is the acceleration due to gravity.

Finally, we can solve for the initial velocity:

v_initial = g * time_to_midpoint / sin(angle)

Now we have all the information needed to find the minimum velocity. We'll use the known values:

g = 32.2 ft/s^2 (acceleration due to gravity)
angle = 20 degrees
distance = 60 ft

1. Calculate the time to reach the midpoint:
time_to_midpoint = (distance) / (v_horizontal)

2. Calculate the initial velocity at the midpoint:
v_initial = (g * time_to_midpoint) / sin(angle)

By plugging in the numerical values, you can find the minimum velocity the outfielder needs to throw the ball.