# Line of sight between two people

## Homework Statement

Mary spots Bill approaching the dorm at a constant rate of 2 m/s on the walkway that passes directly beneath her window, 17 above the ground. When Bill is 120 m away from the point below her window she decided to drop an apple down to him. What is the angle between Mary and Bill at the instant Mary releases the apple?

(There were other parts to this problem, but I got the correct answers to those).

2. The attempt at a solution

Since Bill is 120 m away and the building is 17 m high, tan θ = opp/adj = 120/17, θ = 81.93 degrees

But this is not the right answer :( Any help would be appreciated, thanks!

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TSny
Homework Helper
Gold Member
What is the angle between Mary and Bill at the instant Mary releases the apple?
"The angle between Mary and Bill" is an ambiguous concept. You can imagine a line drawn between Mary and Bill. Not sure what angle is being asked for. The angle between this line and the horizontal? The angle between this line and the vertical?

phinds
Gold Member
2019 Award
If she releases the apple when he is 120m away, he'll keep walking almost 2 minutes after he sees the apple splat on the sidewalk. That, of course, has nothing to do with the math, but does indicate that Mary is not too bright.

Oops, sorry for the confusion. The question asks, what is the angle between the vertical and the line of sight between Mary and Bill?

TSny
Homework Helper
Gold Member
Your calculation looks correct. I agree with phinds regarding Mary's competence. Clearly the apple will hit the ground long before Bill arrives. Are you sure Mary drops the apple when Bill is 120 m away?

Yes, she does. An earlier part of the question asks how long Mary should wait to drop the apple if Bill is to catch it 1.75 m above the ground without speeding up or slowing down - so I had to calculate when she drops it.

The correct answer to the angle problem is 13 degrees - any idea how that could be?

TSny
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Gold Member
So, you calculated that she should drop it when Bill is 120 m away? And that was given to be the correct answer?

No, I calculated that she should drop it when he is 3.6 m away.

TSny
Homework Helper
Gold Member
Ah, good. So, you should use that location for Bill when finding the angle (not the 120 m).

Got it, thanks!

TSny
Homework Helper
Gold Member
Great!