a rocket travels vertically at a speed of 400 km/hr. the rocket is tracked through a telescope by an observer located 9 km from the launching pad. find the rate at which the angle between the telescope and the ground is increasing 3 min after lift-off. (round your answer to two decimal places.)

The rate at which the angle between the telescope and the ground is increasing 3 min after lift-off is 7.48radians per hour.

Step-by-step explanation:

We are given that

A rocket travels vertically at a speed of 400 km/hr. the rocket is tracked through a telescope by an observer located 9 km from the launching pad

Let theta be the angle between the telescope and the ground and the h be the height of the rocket above the ground.

Then

tanθ =

Now we differentiate the trigonometric function with respect to time

= ()

=

..................(1)

Now as we know that the rocket is travelling upwards with a speed of 400 km/hr so the distance it will cover in three minutes will be

400*

tan(theta) =

       = 1 +

       =  

upon substituting this value in the equation (1) we get

          =

          =

/hour

Therefore the rate at which the angle between the telescope and the ground is increasing 3 min after lift-off is 7.48radians per hour.

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step-by-step explanation: