Final answer:
The initial velocity of the model rocket is approximately 55.7 m/s.
Step-by-step explanation:
To find the initial velocity of the model rocket, we can use the equations of projectile motion. The horizontal distance traveled by the rocket is equal to the horizontal component of its initial velocity multiplied by the time of flight. In this case, the horizontal distance is 225 meters and the time of flight can be determined from the vertical motion. Since the rocket lands 100 meters deep in the canyon, we can use the equation d = ut + (1/2)at^2 to find the time it takes to fall. Plugging in the values, we get 100 = 0.5 * 9.8 * t^2, which gives us t = 4.04 seconds. Now, we can use the horizontal distance and time of flight to calculate the initial velocity. The formula for horizontal distance is d = vt, where d is the distance, v is the initial velocity, and t is the time. Rearranging the formula, we get v = d/t. Substituting the values, we get v = 225/4.04 ≈ 55.7 m/s.