Your Open QuestionShow me another »
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.
To find out how fast the rocket is receding from the radar post, we need to use trigonometry and calculus. Here is the step-by-step explanation:
Step 1: Draw a diagram to visualize the problem. Draw a right triangle where the radar post is at one corner, the rocket's location is at another corner, and the 10 km distance between them is the hypotenuse. Label the height of the rocket as 17.32 km and the angle it turns from the vertical as 30 degrees.
Step 2: Using trigonometry, we can determine the distance between the rocket and the radar post when it starts traveling horizontally. This distance can be found using the sine function:
Distance = 17.32 km * sin(30 degrees)
Step 3: Next, we need to find the rate at which the distance is changing. We differentiate this distance with respect to time, using the chain rule of calculus. Since the rocket is traveling horizontally at a constant speed of 12000 km/h, the rate of change of the distance is equal to the rocket's horizontal velocity:
Rate of change of distance = 12000 km/h
Step 4: Finally, we have to calculate the rocket's vertical velocity. We can use the given time interval of 2 minutes (which is equivalent to 2/60 = 1/30 hours). The vertical velocity can be found by dividing the change in height (17.32 km) by the time interval:
Vertical velocity = (17.32 km) / (1/30 hours)
Step 5: Now, we have both the horizontal velocity and the vertical velocity. We can combine them using the Pythagorean theorem to find the total velocity (speed) of the rocket:
Total velocity = sqrt((horizontal velocity)^2 + (vertical velocity)^2)
Step 6: Finally, subtract the rate of change of distance (which is the horizontal velocity) from the total velocity to find how fast the rocket is receding from the radar post:
Receding speed = Total velocity - Rate of change of distance
Plugging in the given values and performing the calculations, you should find that the rocket is receding from the radar post at a speed of 11.2 km/h.