Deriving the Rate of Change of Angle in a Rocket Launch Using Differentiation

[Bostonpancake0]

The question is as follows:

A rocket was launched straight up, and its altitude is given by h = 10 t2 m after t
seconds. You are on the ground 300 m from the launch site watching the rocket going
up. The line of sight from you to the rocket makes an angle θ with the horizontal. By
how many radians per second is θ changing 10 seconds after the launch?


I guess my question is whether my understanding of the problem and working is correct. I'm not 100% confident on my process and my answer and am just wondering if I have missed anything important.

By working and answer is tagged below.

 

[Ash L]

Looks okay when my head is turned sideways. If you want to be picky, you could show working out for how you differentiated to get dh/dt. It's not necessary but the grader might deduct points off that, in which I had suffered first hand experience from that.

 

[Bostonpancake0]

Ahhh yes thanks for that missed it, alright its just that 11degrees a second seems rather large? I tried it another way and got d(theta)/d(t)=60*t/t^4+900...then subbing t gives me d(theta)/d(t)=0.055046 degrees/sec? doesn't this seem like a more likely answer?

 

[Ash L]

I think the left side of your page should be dθ/dh

When t = 5 secs, h = 10(5)^2 = 250m
When t = 10 secs, h = 1000m
When t = 15 secs, h = 2250m
When t = 20 secs, h = 4000m

 

[Mark44]

If you post an image of your work, at least do us the courtesy of posting it right side up instead of rotated 90 deg.

 

[EmmaJoy]

Hi I think I am doing the same assignment as you. I got the same values that dh/dt= 20t, d(theta)/d(h)= 60t/t^4+900 and multiplying them gets d(theta)/d(t)= 1200/109. But I agree, I thought it was too high. But then i tried differentiating d(theta)/d(h) and then subing in h=10t^2 afterward and it got a much lower answer which i believe is correct. Because the original way, we were differentiating dh/dt at the same time as d(theta)/d(h). DON'T FORGET TO CONVERT INTO RADIANS THOUGH! You didn't do this on the sheet. Good luck!