Related Rate (Calc 1): A jet ascends at a 10 degree angle from the horizontal with an airspeed of 550 mi/hr. How fast is the altitude of the jet increasing? If the sun is directly overhead, how fast is the shadow of the jet moving on the ground?

I'm not really sure how to go about working this one. I know that if I froze time at 1 hour I would have a right triangle with a hypotenuse of 550 miles, which I could then use along with the law of sines to find the lengths of the other sides, but I have no clue how to find rate the altitude is increasing.

Question

Related Rate (Calc 1): A jet ascends at a 10 degree angle from the horizontal with an airspeed of 550 mi/hr.  How fast is the altitude of the jet increasing?  If the sun is directly overhead, how fast is the shadow of the jet moving on the ground?

I'm not really sure how to go about working this one.  I know that if I froze time at 1 hour I would have a right triangle with a hypotenuse of 550 miles, which I could then use along with the law of sines to find the lengths of the other sides, but I have no clue how to find rate the altitude is increasing.

anonymous · Answer

Since it's a right triangle, you don't need the law of sines, you just need sin theta.  So for the altitude part, it's just v sin theta.

anonymous · Answer

With the sun overhead, the velocity of the shadow on the ground is calculated in a similar way, using the cosine.  Please don't freeze time.

anonymous · Answer

Yeah, I was worried that if I froze time then I would introduce constants which would prevent me from getting a useful derivative, but I'm still not exactly getting your answer.

anonymous · Answer

You've got a triangle whose "side lengths" are velocities.

anonymous · Answer

oh, so if I have a theta of 10 degrees, and I know the rate the hyp is increasing, then I'm setting it up like sin theta = dy/dt over dh/dt (550)?

anonymous · Answer

Yes, exactly.

anonymous · Answer

ah, thank you.

anonymous · Answer

yw