Final answer:
The initial horizontal velocity of a cannonball fired horizontally is the same as its launch speed (10 m/s), and the vertical velocity is 0 m/s. When fired at a 35° angle, the initial velocities in the horizontal and vertical directions are calculated using trigonometric functions. These concepts help solve various projectile motion problems.
Step-by-step explanation:
When a cannon fires a projectile horizontally at 10 m/s, the initial velocity in the horizontal direction is 10 m/s and the initial velocity in the vertical direction is 0 m/s because there is no vertical component in a horizontal launch. However, when the same cannon launches the projectile at a 35° angle above the ground, the initial velocity must be decomposed into horizontal and vertical components. The horizontal component can be calculated using cos(35°) × 10 m/s, and the vertical component using sin(35°) × 10 m/s.
If we apply these principles to projectile motion problems, for example, when firing a water balloon from a cannon at a 45° angle to hit a target 100 m away, we can use the range equation for projectile motion and solve for the initial speed. Similarly, when analyzing the motion of a projectile launched at an angle, the velocity can be resolved into components to determine distances traveled in the x and y directions over time.