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

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In summary, the goal of this homework problem is to find the angle (theta) that will result in an object being launched the same distance vertically as horizontally. This can be solved using the equations provided, which involve the initial velocity (Vi), the angle (theta), time, and acceleration due to gravity (a). The two equations provided are used to find the range and maximum altitude of the object. The links to these equations are also provided for further reference.
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Xiju
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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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Solving for theta, we get:

theta = arctan(2a/g)

where a is the acceleration due to gravity and g is the gravitational constant. This equation can also be simplified to:

theta = 2arctan(1)

which gives us:

theta = 2(45 degrees)

Therefore, the angle at which the object needs to be launched is 45 degrees. This can also be verified by plugging in the values for Vi and t in the equations above and solving for theta.

I hope this helps. Let me know if you have any further questions.
 

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

1. What was the question that your teacher couldn't answer?

The specific question that my teacher couldn't answer may vary, but typically it is related to a specific scientific concept or problem.

2. Did you ask your teacher for help before seeking assistance elsewhere?

Yes, it is always best to first ask your teacher for help since they are the most knowledgeable about the subject and can provide tailored explanations and guidance.

3. What resources did you use to find the answer?

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