Question

Dennis is up to bat during his softball game. he swings his bat 261 degrees in 0.75 seconds before contacting the ball. he makes contact with the ball 57 cm down the bat (away from the axis of rotation). what is the linear velocity of the ball after contact with the bat? (please put the answers in meters)

Answer 1

here is answer

Explanation:

To find the linear velocity of the ball after contact with the bat, we need to convert the angular velocity to linear velocity.

Given:

Angular displacement (θ) = 261 degrees

Time (t) = 0.75 seconds

Distance from axis of rotation (r) = 57 cm

First, we convert the angular displacement from degrees to radians:

θ (in radians) = (261 degrees) × (π/180)

≈ 4.5539 radians

Next, we calculate the angular velocity (ω):

ω = θ / t

= 4.5539 radians / 0.75 seconds

≈ 6.0719 radians/second

To convert the distance from the axis of rotation to meters:

r (in meters) = 57 cm × (1 meter / 100 centimeters)

= 0.57 meters

Now, we can calculate the linear velocity (v) using the formula:

v = ω × r

v ≈ 6.0719 radians/second × 0.57 meters

v ≈ 3.4649 meters/second

Therefore, the linear velocity of the ball after contact with the bat is approximately 3.4649 meters/second.