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A projectile is launched with speed v at an angle alpha above the horizontal. After time t, as seen from the launch point, the projectile appears to be at an angle of elevation beta. Which of the following statements is/are correct?

1. The y-coordinate of the projectile at time t is (v*sin(alpha))*t - (1/2)*g*t²
2. The x-coordinate of the projectile at time t is (v*cos(alpha))*t
3. tan(beta) = tan(alpha) - g*t / (2*v*cos(alpha))
4. The speed of projection is g*t*cos(beta) / (2*sin(alpha - beta))

Correct answer: The y-coordinate of the projectile at time t is (v*sin(alpha))*t - (1/2)*g*t²

Solution

Options A and B are the standard projectile coordinates and are correct. For option C: tan(beta) = y/x = tan(alpha) - gt/(2v*cos(alpha)), also correct. For option D: using the formula for v, v = gt*cos(beta)/(2*sin(alpha-beta)) can be derived from the geometry, making D also correct.

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