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Alvan M.

Test Engineer. Tutor for two years

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Mechanical Engineering

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Question:

If the magnitude of the resultant force of two equal forces, then at what angle did the first two forces meet?

Alvan M.

Answer:

120 degrees. We can solve this using the law of cosines which says that for any triangle C^2 = A^2 + B^2 + 2ABcos(theta). Since A, B, and C are all equal (we'll call them P): P^2 = P^2 + P^2 + 2P^2cos(theta), divide the entire equation by P^2 1 = 2+2cos(theta), subtract 2 from both sides -1 = 2cos(theta), divide both sides by 2 -1/2 = cos(theta), invert the cosine arccos(-1/2) = theta 120 degrees = theta

Algebra

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Question:

Solve for x: 16 = x^2-8x+32

Alvan M.

Answer:

x^2 - 8x + 32 = 16, subtract 16 from both sides to make the quadratic equal to 0 x^2 - 8x + 16 = 0, factor the equation. (x-4)*(x-4) = 0, you can verify this step by multiplying the components out (x-4)^2 = 0, take the square root of both sides x-4 = 0, add 4 to both sides x = 4

Physics

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Question:

An apple on earth is dropped at the same time, and at the same speed as an identical one dropped on the moon. Which apple hits the ground first?

Alvan M.

Answer:

The apple on the earth because the acceleration due to gravity of earth is higher than that on the moon. You can calculate exactly how fast each apple lands using the kinetic equation h = h0 + v0*t + a*(t^2), where h is the height of the ground, h0 is the initial height of the apple, v0 is it's initial velocity, zero, and a is the acceleration due to gravity.

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