Final answer:
To calculate the final velocity of the bowling ball, we need to break down the initial velocity into its x and y components using trigonometry. We can then use the law of conservation of momentum to find the final velocity magnitude, and trigonometry again to find the direction of the final velocity.
Step-by-step explanation:
To calculate the final velocity of the bowling ball, we need to break down the initial velocity of the ball into its x and y components. Using the given angle of 83.5 degrees, we can use trigonometry to find the x and y components. The x component can be found by multiplying the initial velocity (9.4 m/s) by the cosine of the angle, and the y component can be found by multiplying the initial velocity by the sine of the angle.
After the collision, we can use the law of conservation of momentum to calculate the final velocity of the bowling ball. The initial momentum before the collision is equal to the final momentum after the collision. Since only the pin is scattered, we can assume the final mass of the bowling ball is still 6.25 kg. By plugging in the initial and final mass, as well as the initial and final velocities, we can solve for the final velocity magnitude.
To find the direction of the final velocity, we can use trigonometry again. Since the final velocity has both x and y components, we can use the arctan of the ratio of the y component to the x component to find the angle.