Final answer:
To find the speed of the ball, use the concept of circular motion. The angular velocity remains constant since the ball is moving at a constant speed. Use the formula v = ω * r, where ω is the angular velocity and r is the radius of the circle. Substituting the given values, the speed of the ball is approximately 0.24 m/s.
Step-by-step explanation:
To find the speed of the ball, we can use the concept of circular motion. The ball is swung in a horizontal circle and makes an angle of 14 degrees with the vertical. Since the ball is moving at a constant speed, its angular velocity remains constant. We can use the relationship between angular velocity and linear velocity to find the speed of the ball. The formula for angular velocity is given by:
ω = v/r
where ω is the angular velocity, v is the linear velocity, and r is the radius of the circle. In this case, the radius is the length of the string, which is 0.8m. Rearranging the formula, we get:
v = ω * r
The angle made by the ball with the vertical is 14 degrees. We can convert this angle to radians by multiplying it by π/180. So, the angle in radians is (14*π)/180. The angular velocity is the rate at which the angle changes with time. Since the ball is moving at a constant speed, the angular velocity is constant. Therefore, we can use the given angle of 14 degrees to find the angular velocity. Now substituting the values in the formula:
v = (14*π/180) * 0.8
Simplifying the equation, we get:
v ≈ 0.24 m/s
So, the speed of the ball is approximately 0.24 m/s.