Wednesday, January 9, 2013

Determining the Angle for which Height and Range would be Equal

...without having to know any trigonometric identities.

take any example for the velocity of y when gravity equals 9.8 m/s, like for you earthers:
eg. 

Vy = 50 m/s

50/4.9 = Range time


= height (as well as range)


= Vx



Vy/Vx arctan = angle = 75.96 degrees

we find that regardless of what gravity is, for the height and range to be equal the ratio of Vy/Vx will always be 4:1 and hence have the same angle on any planet in the known universe.

*note - if you need the range to be a certain amount more than the height, multiply Vx by that amount. for example, if the range is 2.5 times more than the height, multiply Vx by 2.5.

if you need the height to be a certain amount more than the range, divide the range by that amount. for example, if the height is 2.5 times more than the range, divide the range by 2.5.

2 comments:

Thuy Nguyen said...

I don't understand why you divide vertical velocity with half of acceleration.

dwdeclare said...

@Thuy Nguyen

50m/s divided by 9.8 is the time the object takes to achieve its maximum height. so dividing by 1/2 of gravity would equal the range time.

2Vy/9.8 also works.

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