Understanding the Physics

* Projectile Motion: The cannonball's motion is a classic example of projectile motion, where gravity acts as the only force influencing its vertical motion.

* Symmetry: The trajectory of a projectile is symmetrical. The initial velocity at launch is equal in magnitude to the final velocity when it reaches the same height (in this case, the height of the balloon).

Solution

Since the cannonball hits the balloon at the top of its trajectory, it means it has reached its maximum height. At this point, the vertical component of its velocity is zero. However, the horizontal component of the velocity remains constant throughout the flight (neglecting air resistance).

1. Horizontal Velocity:

* The initial horizontal velocity (v_x) is calculated using:

v_x = v * cos(θ)

where:

* v is the initial velocity (141 m/s)

* θ is the launch angle (45 degrees)

* v_x = 141 m/s * cos(45°) = 99.8 m/s (approximately)

2. Final Velocity:

* Since the horizontal velocity remains constant, the final velocity of the cannonball when it hits the balloon is equal to its horizontal velocity:

v_final = v_x = 99.8 m/s

Therefore, the cannonball is going approximately 99.8 m/s when it hits the balloon.