1. Problem: Find the horizontal and vertical components of the initial velocity of a ball tossed at 16 degrees with a resultant velocity of 12 m/s. 2. Formula: For velocity components, use $$v_x = v \cos(\theta)$$ $$v_y = v \sin(\theta)$$ where $v$ is the resultant velocity and $\theta$ is the angle above the horizon. 3. Calculate horizontal component: $$v_x = 12 \cos(16^\circ)$$ $$v_x = 12 \times 0.9613 = 11.5356$$ 4. Calculate vertical component: $$v_y = 12 \sin(16^\circ)$$ $$v_y = 12 \times 0.2756 = 3.3072$$ 5. Problem: A football launched at 45.11 degrees travels 33 m horizontally in 2.6 s. Find initial horizontal and vertical velocities and resultant velocity. 6. Horizontal velocity from distance and time: $$v_x = \frac{33}{2.6} = 12.6923$$ 7. Using angle to find vertical velocity: $$v_y = v_x \tan(45.11^\circ)$$ $$v_y = 12.6923 \times 1.002 = 12.7167$$ 8. Resultant velocity magnitude: $$v = \sqrt{v_x^2 + v_y^2}$$ $$v = \sqrt{12.6923^2 + 12.7167^2} = \sqrt{161.1 + 161.7} = \sqrt{322.8} = 17.97$$ 9. Problem: Ali's high jump initial vertical velocity is 3.5 m/s, center of gravity 1.16 m above ground. The question is incomplete, so no calculation is done. Final answers: a) Horizontal component ball: $11.54$ m/s b) Vertical component ball: $3.31$ m/s Second problem: a) Initial horizontal velocity football: $12.69$ m/s b) Initial vertical velocity football: $12.72$ m/s c) Resultant velocity football: $17.97$ m/s