Angle of a projectile which maximizes the range? Cannot solve the equation?

R for this specific problem is R = (Vacos(theta) - Vc)*(2Vasin(theta))/g

where V_a is the velocity of the arrow, which is shot off of the car

V_c is the velocity of the car, which is moving in the opposite direction of the arrow

So, to find the angle I need the derivative and set it equal to 0

therefore

2V_a/g * [2V_a cos^2(theta) - V_c cos(theta) - V_a] = 0

How do I Solve it??

1 Answer

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  • 9 years ago
    Favorite Answer

    The answer is 45°. Consider the trigonometric functions in the equation, since it is the only part related to the angle. It will finally go to a product of variables that are not influenced by angle and Cot theta. The more the value of cot theta, the higher the range. The maximum value you can have is 1. Cot inv1 = 45°.

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