Question: A physics student on Planet Exidor throws a ball, and it follows the parabolic trajectory shown in The trajectory is shown on the xy plane. It is a concave curve starting at the origin, marked as 0 seconds. The highest point of the trajectory is marked as 2.0 seconds. Point marked as 1.0 second is located on the ascending branch. Point marked as 3.0 seconds is located on the descending branch. The ball's position is shown at 1.0 s intervals until t = 3.0 s. At t = 1.0 s the ball's velocity has components $v_x = 2.0$ m/s, $v_y = 2.2$ m/s. Determine the x- and y-components of the ball's velocity at $t = 0.0$ s.

1. **Problem Statement:** A ball is thrown on Planet Exidor and follows a parabolic trajectory. At $t=1.0$ s, the velocity components are $v_x = 2.0$ m/s and $v_y = 2.2$ m/s. The highest point is at $t=2.0$ s. We need to find the velocity components at $t=0.0$ s. 2. **Key Concepts and Formulas:** - The horizontal velocity component $v_x$ remains constant in projectile motion without air resistance. - The vertical velocity component $v_y$ changes due to acceleration from gravity $g$. - The velocity at time $t$ is given by: $$v_x(t) = v_{x0}$$ $$v_y(t) = v_{y0} - g t$$ - At the highest point ($t=2.0$ s), vertical velocity $v_y = 0$. 3. **Find the acceleration due to gravity $g$ on Planet Exidor:** At $t=2.0$ s, $v_y = 0$, so: $$0 = v_{y0} - g \times 2.0$$ $$v_{y0} = 2 g$$ 4. **Use velocity at $t=1.0$ s to find $v_{y0}$ and $g$:** Given at $t=1.0$ s: $$v_y(1) = v_{y0} - g \times 1 = 2.2$$ Substitute $v_{y0} = 2 g$: $$2 g - g = 2.2$$ $$g = 2.2$$ 5. **Calculate $v_{y0}$:** $$v_{y0} = 2 g = 2 \times 2.2 = 4.4$$ 6. **Horizontal velocity $v_x$ is constant:** $$v_x(0) = v_x(1) = 2.0$$ 7. **Final answer:** - $v_x(0) = 2.0$ m/s - $v_y(0) = 4.4$ m/s Thus, the velocity components at $t=0.0$ s are $v_x = 2.0$ m/s and $v_y = 4.4$ m/s.