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From a hilltop to the west of Willy, Oompa Loompas launch gum balls out of slingshots toward his canoe. These gum balls travel in a linear path, dropping 3.2 meters as they travel eastward 15.3 meters to strike the canoe. 1. What's the distance from the Oompa Loompas to the canoe? 2. What is the angle, measured from the horizon, that the Oompa Loompas are firing from? 3. Is it possible for a sling sot propelled gumball to travel in a linear path? If not, what is the flaw in this logic?
If I have it drawn right, part a is the pyth. theorem.
|dw:1360440654830:dw|

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Maybe law of sines for part two?
I am not very good in English, but if your pic is correct, you found the distance right.
Thanks so much! I think I drew it right. @Jonask what do you think?
yes for 2|dw:1360448299629:dw|
Awesome. Could I take the arctan?
Whoops, no. I ment the law of sines.
\(\theta\) on the @Jonask 's pic is not measured from the horizon.
No matter which angle you search, the law of sines is a ratio, it is mainly used to to find specific sides, but in such a right-angled triangle, as it seems (only judging by the picture - I haven't fully read the problem) you wouldn't want to use that law, more likely the regular trigonometric functions and solve for the angle.
Where is the horizon?
I wonder if it is a right triangle, from part 4.
|dw:1360441416725:dw|
Oh boy.
yes its like an angle of elevation @klimenkov |dw:1360448668700:dw|
yippee. So where do I go from here?
1st of all, is the pic 100% correct?
I really think the drawing is right. I really think the distance is right I do not know about part two, how to get the angle And I am unsure about the logic part 4.
*part 3
Anybody?
tan theta=3.2/15.3
not theta but alpha\[\tan \alpha=3.2/15.3\]
That is 0.00365.
now to get alpha use arctan(0.00365)
That is 0.209129
Thanks @Jonask
Now for the next part///
first of all gravity wont allow the ball just to down at the same angle without pulling it towards the earth 2nd air resistance especially because the horizontal distance is too big compared to the vertical
I was thinking the same, had it wrote down. Wanted to verify. Thanks SOO much.
So what needed to be done to find the angle from the horizon?
its that arctan 0.00365=0.209 degrees this also accounts for the balls imppsossible perpetual linear motion
Thanks and God Bless. Keep on living for Jesus.
God Bless you too @AmTran_Bus
Looks correct.

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