In lacrosse, a ball is thrown from a net on the end of stick by rotating the stick and forearm about the elbow. If the angular velocity of the ball about the elbow joint is 30.3 rad / s and the ball is 1.35 m from the elbow joint, what is the velocity of the ball?
Well, I gotta hand it to you, that's quite the swinging question! Let's do some math-juggling to find the velocity of the ball in lacrosse.
First things first, we need to find the linear velocity of the ball. To do that, we can use the formula:
v = ω * r
where v is the linear velocity, ω is the angular velocity, and r is the distance from the axis of rotation (which in this case is the elbow joint).
So, plugging in the values you've given me, the linear velocity of the ball would be:
v = 30.3 rad/s * 1.35 m ≈ 40.905 m/s
So, my friend, the velocity of the ball would be approximately 40.905 meters per second. Watch out, goalies! That ball's coming in hot!
To find the velocity of the ball, we need to use the formula:
velocity = angular velocity x radius
Given:
angular velocity (ω) = 30.3 rad/s
radius (r) = 1.35 m
Substituting the given values into the formula:
velocity = 30.3 rad/s x 1.35 m
velocity = 40.905 m/s
Therefore, the velocity of the ball is approximately 40.905 m/s.
To find the velocity of the ball, we can use the relationship between linear velocity and angular velocity. The formula is:
v = r * w
where v is the linear velocity, r is the distance from the rotation axis (in this case, the elbow joint) to the point of interest (in this case, the ball), and w is the angular velocity.
Given:
Angular velocity (w) = 30.3 rad/s
Distance from elbow joint to ball (r) = 1.35 m
Plugging in the values into the formula, we get:
v = 1.35 m * 30.3 rad/s
Now let's calculate the velocity:
v = 40.905 m/s
Therefore, the velocity of the ball is approximately 40.905 m/s.