A model rocket is launched with an initial velocity of 10 m/sec at an angle of 45° to the ground. What is the total time of flight? What is the highest point in its trajectory? What is the horizontal range achieved?

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To find the total time of flight, highest point in its trajectory, and the horizontal range achieved by the model rocket, we can break down the problem into different components and use basic equations of motion.

1. Total Time of Flight:
The total time of flight is the duration for which the rocket is in the air. To find it, we need to consider the rocket's vertical motion. We can calculate this using the formula for time of flight, which is given by:

Time of Flight (T) = (2 * initial vertical velocity * sin(angle of projection)) / acceleration due to gravity

Given:
Initial vertical velocity (Vi_y) = 10 m/s * sin(45°) = 7.07 m/s
angle of projection = 45°
acceleration due to gravity (g) = 9.8 m/s²

Plugging in the values:

T = (2 * 7.07 m/s) / 9.8 m/s²
≈ 1.44 seconds

Therefore, the total time of flight is approximately 1.44 seconds.

2. Highest Point in its Trajectory:
The highest point in the rocket's trajectory can be determined by analyzing its vertical motion. At the highest point, the vertical velocity becomes zero. We can use the formula for vertical displacement to find the highest point, which is given by:

Vertical Displacement (H) = (initial vertical velocity)^2 * sin^2(angle of projection) / (2 * acceleration due to gravity)

Given:
Initial vertical velocity (Vi_y) = 10 m/s * sin(45°) = 7.07 m/s
angle of projection = 45°
acceleration due to gravity (g) = 9.8 m/s²

Plugging in the values:

H = (7.07 m/s)^2 * sin^2(45°) / (2 * 9.8 m/s²)
≈ 2.55 meters

Therefore, the highest point in its trajectory is approximately 2.55 meters.

3. Horizontal Range Achieved:
The horizontal range achieved by the rocket is the horizontal distance traveled by it from launch to landing. We can calculate this using the formula for horizontal range, which is given by:

Horizontal Range (R) = initial horizontal velocity * total time of flight

Given:
Initial horizontal velocity (Vi_x) = 10 m/s * cos(45°) = 7.07 m/s (as the rocket is initially launched at an angle of 45°)
Total time of flight (T) ≈ 1.44 seconds (calculated earlier)

Plugging in the values:

R = 7.07 m/s * 1.44 s
≈ 10.16 meters

Therefore, the horizontal range achieved is approximately 10.16 meters.