A couple of projectile trajectory-related questions

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SUMMARY

The discussion centers on determining the angle theta at which the horizontal and vertical components of a vector are equal in magnitude. The correct answer is 45 degrees, as this angle results in two congruent angles in a right triangle, fulfilling the condition of equal components. The user confirms their reasoning by illustrating the relationship between the angles and the right triangle's properties. No specific equations are provided, emphasizing a conceptual understanding of vector components.

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First one (to check with others on whether or not it's correct, although I'm sure it's very easy)

Homework Statement


A vector makes an angle, theta, with the horizontal. The horizontal and vertical components of the vector will be equal in magnitude if angle theta is
Four Choices
(1) 30 degrees
(2) 45 degrees
(3) 60 degrees
(4) 90 degrees

Homework Equations


None I believe

The Attempt at a Solution


1. I drew out a right triangle
2. Angle theta is located at the left portion of the right triangle
3. Right angle = 90 degrees, of course
4. Two congruent angles will have congruent sides; as a result, 45 degrees is my answer (also because the two angles have to be equal and must add up to 90).

I'll add another one in a bit after I get this out of the way.
 
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