Final answer:
To calculate the total horizontal distance covered by the rocket, we need to find the horizontal components of each segment of its motion and add them up. The rocket covers 0 km horizontally in the first segment, 5.34 km in the second segment, and 26.43 km in the third segment. Adding up these distances gives a total horizontal distance of 31.77 km.
Step-by-step explanation:
To find the total horizontal distance covered by a rocket, we need to calculate the horizontal components of each segment of its motion and then add them up.
For the first segment, the rocket flies 10 km vertically, so the horizontal distance covered is 0 km.
For the second segment, the rocket flies 20 km at an angle of 15° to the vertical. The horizontal distance covered can be calculated using the formula: horizontal distance = vertical distance * tan(angle). So, the horizontal distance is 20 km * tan(15°) = 5.34 km.
For the third segment, the rocket flies 60 km at an angle of 26° to the vertical. Using the same formula, the horizontal distance covered is 60 km * tan(26°) = 26.43 km.
Adding up the horizontal distances from each segment, the total horizontal distance covered by the rocket is 0 km + 5.34 km + 26.43 km = 31.77 km.
Therefore, the correct answer is option d) 100 km.