What Angle Makes a Projectile Travel Equally in X and Y Directions?

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To determine the angle (theta) for a projectile to travel the same distance vertically and horizontally, the equations of motion for both axes must be equated. The vertical distance is given by ViSin(theta)(time) - 1/2at^2, while the horizontal distance is ViCos(theta)(2time). By setting these equations equal, one can solve for theta. The key relationship is that the range (R) equals the maximum altitude (h), leading to the conclusion that the initial vertical velocity (vyo) is equal to the initial velocity (vo) multiplied by Sin(theta). This establishes the necessary angle for equal distances in both directions.
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Homework Statement


I need to find the angle (theta) that when an object is launched from it, it will go the same distance vertically as horizontally. So if it went 100 feet up in the Y axis it also went 100 feet in the X axis. Thanks.
ps. can you show me how you got this answer?


Homework Equations


ViSin(theta)(time) - 1/2at^2 = delta Y

ViCos(theta) (2time) = delta X

The Attempt at a Solution


ViSin(theta)(time) - 1/2at^2 = ViCos(theta) (2time)
 
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