A rocket is being tracked from a radar post that is 10 km from the launch pad.the rocket arises vertically at a height of 17.32 km and then turns at an angle of 30 degrees fron the vertical directly away from the radar post .it then travels at the constant speed of 12000 km/h along a straight path for 2 min. How fast is it recedding from the radar post ?
To find out how fast the rocket is receding from the radar post, we need to break down the problem into smaller parts and use trigonometry.
Let's consider the initial position of the rocket, its position after turning at an angle, and the position after traveling for 2 minutes.
1. Initial position: The rocket's initial position is at a height of 17.32 km directly above the launch pad. Since the radar post is 10 km away from the launch pad, the distance between the radar post and the rocket at this point is the hypotenuse of a right-angled triangle with sides 10 km and 17.32 km (height of the rocket). Using the Pythagorean theorem, we can calculate the distance between the radar post and the rocket at this point:
Distance = √(10^2 + 17.32^2) km
2. Position after turning at an angle: After turning at an angle of 30 degrees from the vertical, the rocket would have moved horizontally as well. Since the rocket turns directly away from the radar post, the horizontal distance it moves away from the radar post is equal to the distance calculated in the previous step.
3. Position after traveling for 2 minutes: The rocket travels at a constant speed of 12,000 km/h along a straight path for 2 minutes. To calculate the horizontal distance traveled by the rocket, we can multiply its speed by the time:
Distance = (12,000 km/h) * (2/60) h
Now, we can calculate the total distance between the radar post and the rocket after considering these three stages. The rocket's speed receding from the radar post can be found by differentiating this distance with respect to time.
Finally, the rate at which the rocket is receding from the radar post can be calculated by taking the magnitude of the derivative of the total distance with respect to time.