Velocity Components 08E150

1. **State the problem:** We need to find the x- and y-components of the velocity of a ball at time $t = 2.0$ seconds. 2. **Identify the formulas:** - The velocity in the x-direction, $v_x$, is usually constant if no horizontal acceleration is present. - The velocity in the y-direction, $v_y$, changes due to gravity and is given by $$v_y = v_{y0} - g t$$ where $v_{y0}$ is the initial vertical velocity, $g$ is the acceleration due to gravity (approximately $9.8$ m/s$^2$), and $t$ is time. 3. **Assumptions:** - If initial velocities are not given, assume initial horizontal velocity $v_{x0}$ and initial vertical velocity $v_{y0}$ are known or given. 4. **Calculate $v_x$:** - Since horizontal velocity is constant, $$v_x = v_{x0}$$ 5. **Calculate $v_y$:** - Using the formula $$v_y = v_{y0} - g t$$ - Substitute $t = 2.0$ s and $g = 9.8$ m/s$^2$. 6. **Final answer:** - The x-component of velocity at $t=2.0$ s is $$v_x = v_{x0}$$ - The y-component of velocity at $t=2.0$ s is $$v_y = v_{y0} - 9.8 \times 2.0 = v_{y0} - 19.6$$ If you provide the initial velocities, I can calculate numerical values.