Final answer:
a) The final velocity in the x-direction is 1.92 m/s. b) The final velocity in the y-direction is 2.29 m/s. c) The final velocity is 3.02 m/s and the angle of impact is 52.09°.
Step-by-step explanation:
a) The final velocity in the x-direction can be calculated using the formula v_x = v_initial * cos(theta), where v_initial is the initial velocity and theta is the angle of impact. In this case, the initial velocity is 3.00 m/s and the angle of impact is 50°. Plugging in these values, we get v_x = 3.00 m/s * cos(50°) = 1.92 m/s. Therefore, the final velocity in the x-direction is 1.92 m/s.
b) The final velocity in the y-direction can be calculated using the formula v_y = v_initial * sin(theta), where v_initial is the initial velocity and theta is the angle of impact. Plugging in the values, we get v_y = 3.00 m/s * sin(50°) = 2.29 m/s. Therefore, the final velocity in the y-direction is 2.29 m/s.
c) The final velocity can be calculated using the Pythagorean theorem: v_final = sqrt((v_x^2) + (v_y^2)). Plugging in the values, we get v_final = sqrt((1.92 m/s)^2 + (2.29 m/s)^2) = 3.02 m/s. The angle of impact can be calculated using the inverse tangent function: theta = arctan(v_y / v_x). Plugging in the values, we get theta = arctan(2.29 m/s / 1.92 m/s) = 52.09°. Therefore, the final velocity is 3.02 m/s and the angle of impact is 52.09°.