In a fast-pitch softball game the pitcher is impressive to watch, as she delivers a pitch by rapidly whirling her arm around so that the ball in her hand moves in a circle. in one instance, the radius of the circle is 0.681 m. at one point on this circle, the ball has an angular acceleration of 67.7 rad/s^2 and an angular speed of 18.6 rad/s. (a) find the magnitude of the total acceleration (centripetal plus tangential) of the ball. (b) determine the angle of the total acceleration relative to the radial direction.

(a). The magnitude of the total acceleration of the ball is 239.97 m/s².

(b). The angle of the total acceleration relative to the radial direction is 11.0°

Explanation:

Given that,

Radius of the circle = 0.681 m

Angular acceleration = 67.7 rad/s²

Angular speed =18.6 rad/s

We need to calculate the centripetal acceleration of the ball

Using formula of centripetal acceleration

Put the value into the formula

We need to calculate the tangential acceleration of the ball

Using formula of tangential acceleration

Put the value into the formula

(a). We need to calculate the magnitude of the total acceleration of the ball

Using formula of total acceleration

Put the value into the formula

(b). We need to calculate the angle of the total acceleration relative to the radial direction

Using formula of the direction

Put the value into the formula

Hence, (a). The magnitude of the total acceleration of the ball is 239.97 m/s².

(b). The angle of the total acceleration relative to the radial direction is 11.0°

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