Final answer:
The final velocity (magnitude and direction) of the struck ball is 15 m/s and at an angle of 135°.
Step-by-step explanation:
First, we need to find the initial momentum of the tennis ball. Momentum is the product of mass and velocity. The mass of the tennis ball is 200 g, or 0.2 kg, and its initial velocity is 15 m/s. Therefore, the initial momentum of the tennis ball is:
Momentum = mass × velocity = 0.2 kg × 15 m/s = 3 kg·m/s
Next, we need to use the principle of conservation of momentum to find the final velocity (magnitude and direction) of the struck ball. Since the two balls have equal masses, the final momentum of the struck ball will be equal to the initial momentum of the tennis ball.
Final momentum of the struck ball = 3 kg·m/s
Lastly, to find the final velocity of the struck ball, we can use the final momentum and its mass. The mass of the struck ball is also 200 g, or 0.2 kg. Therefore, the magnitude of the final velocity of the struck ball is:
Final velocity = final momentum / mass = 3 kg·m/s / 0.2 kg = 15 m/s
Since the tennis ball was scattered at an angle of 45° from its original direction, we can determine the direction of the struck ball by subtracting 45° from 180°:
Final direction of the struck ball = 180° - 45° = 135°
Therefore, the final velocity (magnitude and direction) of the struck ball is 15 m/s and at an angle of 135°.