Question
A rugby player passes the ball 7.00 m across the field, where it is caught at the same height as it left his hand. (a) At what angle was the ball thrown if its initial speed was 12.0 m/ s, assuming that the smaller of the two possible angles was used? (b) What other angle gives the same range, and why would it not be used? (c) How long did this pass take?
1. $14.2^\circ$
2. $75.8^\circ$
3. $0.60 \textrm{ s}$

# OpenStax College Physics, Chapter 3, Problem 30 (Problems & Exercises)

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Why is gravity a positive value? I see in the end result, it should be a positive value or else we have a negative angle, but how are we supposed to know when we consider gravity a negative or positive value?

Hi georgeh, thanks for the question. The variable $g$ is meant to always be positive. It's the magnitude of the acceleration due to gravity. In some questions, sure enough, 'gravity' is negative, but that's represented by a negative sign explicitly in front of $g$. When using one of the regular kinematics equations where you have a factor $a$, where $a$ is the 'acceleration due to gravity, this would get replaced by $-g$ (assuming you're working with a coordinate system where down is negative). I can totally see how this gets confusing, since $g$ is also commonly named 'the acceleration due to gravity'! The full, proper name for $g$ should be the magnitude of the acceleration due to gravity, but that's too wordy, so it's call 'acceleration due to gravity' for short.

The equation used here is the range equation. It is not one of the regular kinematics equations. It contains $g$ with no negative sign in front. $g$ is always positive since it's a magnitude.

Hope this helps,
Shaun

Hello Sean,

Thank you for your ongoing help. I have one question... at the end of this problem we divide x by Vox. (7/vox) with Vox being 12sin(14.2) to which I get 2.9437. Therefore, I plugged this in and took 7/2.9437 = 2.37797. I am unsure why you got 0.60s. I see on the image from your calculator that you did 12/cos(14.2)... can you explain why please?

No worries at all. Sometimes stepping away from a problem, then returning to it later, is the best problem solving tip if you've been working at problems for a while. The brain sometimes needs a rest, and it's always churning away at finding solutions even when you're doing other things like going for a walk.

I have a question regarding the inverse sin function. I have tried many different ways to type the equation into my calculator, but I am unable to get 14.2 degrees. When I hit the inverse sin function and put in (68.6/12) it keeps giving domain error. Is there a way to set up the equation to avoid this? Thanks.