Projectile motion Q

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From a canon standing on a 100m height platform, a blue ball (launched at 60 degrees) and a white ball (launched at 30 degrees) both have an initial velocity of 50 m/s. Why is it that the white ball would have a smaller max height and longer range (answer according to berkeley review)

I mean...i get the max height part since (vsin30)^2/2g < (vsin60)^2/2g....but Im confused about the range since since it takes less time for the white ball to reach its max height.

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They will both travel the same horizontal distance. I don't know why the book said one will go farther than the other. The equation for range is:

R = [(v0)^2 * sin(2ø)]/g

sin(120&#730;)=sin(60&#730;), and the initial height is not a factor in the equation, so they will be equal. A less technical, but more intuitive way to look at it, for me anyway, is that you know the maximum range will be at 45&#730;. Anything above or below that will have a shorter range. If one is being launched 15&#730; above and one 15&#730; below, then they will go the same distance.

I was surprised to see that the book gave a different answer, since I have been studying it this way the whole time. Please correct me if I am wrong.
 
I actually just crunched the numbers, and the book is right. The one that starts at 30&#730; does travel a farther x distance. I guess my reasoning doesn't hold when you are starting from a height. Good to know!

Sorry for any confusion!
 
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I actually just crunched the numbers, and the book is right. The one that starts at 30&#730; does travel a farther x distance. I guess my reasoning doesn't hold when you are starting from a height. Good to know!

Sorry for any confusion!

Yea when they are complementary angles they will travel the same horizontal distance but this only applies when the initial position and the final position are at the same height.
 
dang...so basically its something you gotta memorize or else you're forced to use the quadratic equation huh?
 
in what cases could the total flight time formula be used: t= v0sin(theta)/g times 2

and when can that range formula be used?

sometimes it gives me the right answer and sometimes it doesnt work
 
I've never used that time formula, but the range one can only be used if the starting and final heights are the same...learned that today ;)
 
also, do you just subtract 180-120 to find that its equal to sin 60? i forgot all that pi circle stuff!
 
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