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Calculuss homeworrk heelp?
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 ?the answer is suppose to be 11.2 km/h . Can you show me all the work so i can understand the questins.It means a lot lot and Thank you guys who are out there helping people understand.

Certainly! Let's break down the problem step by step to find the solution.

First, let's draw a diagram to visualize the situation. We have a radar post (R), a launch pad (L), and the rocket's position (P) after it turns at an angle of 30 degrees from the vertical. The distance between the radar post and the launch pad is 10 km, and the rocket's height is 17.32 km.

```
R
/
/
/
/_ _
L P
```

Now, let's find the distance between the radar post and the rocket's position after it turns. We can use the Pythagorean theorem. The horizontal component is equal to the distance between the radar post and the launch pad (10 km), and the vertical component is equal to the rocket's height (17.32 km).

```
Distance = sqrt((Horizontal Component)^2 + (Vertical Component)^2)
= sqrt((10 km)^2 + (17.32 km)^2)
≈ 20 km
```

Therefore, the distance between the radar post and the rocket's position after it turns is approximately 20 km.

Next, let's calculate the time it takes for the rocket to travel along the straight path for 2 minutes. We know that speed is equal to distance divided by time. In this case, the speed is constant at 12000 km/h.

```
Speed = Distance / Time
12000 km/h = 20 km / Time
Time = 20 km / 12000 km/h
Time = 1/600 hours
```

So, the rocket travels along the straight path for 1/600 hours.

Finally, let's find the rate at which the rocket is receding from the radar post. We can use the concept of relative velocity. The rocket's velocity comprises two components: the horizontal component (towards the radar post) and the vertical component (perpendicular to the radar post).

Since the rocket is receding from the radar post, we only need to consider the horizontal component. The rate at which the rocket is receding is equal to the horizontal component of the rocket's velocity.

To find the horizontal component, we need to find the rocket's horizontal displacement during the 2-minute interval. The rocket travels at a constant speed of 12000 km/h. We can calculate the horizontal displacement using the formula:

```
Distance = Speed * Time
= 12000 km/h * (1/600 hours)
= 20 km
```

Therefore, the rocket's horizontal displacement during the 2-minute interval is 20 km.

Now we can find the rate at which the rocket is receding by dividing the horizontal displacement by the time taken:

```
Rate = Displacement / Time
= 20 km / (1/600 hours)
= 12000 km/h
```

So, the rocket is receding from the radar post at a rate of 12000 km/h.

Apologies, I made an error in my previous response. The correct answer is 12000 km/h, not 11.2 km/h.

I hope this explanation helps you understand the question. If you have any further questions, feel free to ask!