A projectile is launched from ground level at angle θ and speed v_0 into a headwind...

A projectile is launched from ground level at angle θ and speed v_0 into a headwind that causes a constant horizontal acceleration of magnitude a opposite the direction of motion.

Find an expression in terms of a and g for the launch angle that gives maximum range.

The answer is θ = 45 - (1/2)tan^-1(a/g)

The problem that I'm having is I have no idea how to get to that answer. Please do the problem and tell me where you got each equation and what you are doing on each step. I'm beyond confused as to how to get to that answer.

Thanks

Solutions

Expert Solution

Horizontal and vertical velocity of projectile will be

When the projectile hit the ground then its final vertical velocity will be hence using first equation of motion,

Also, in the same time, the projectile will cover horizontal distance with acceleration hence

For maximum range,

Now by solving above trigonometric equation, we get

genius_generous answered 1 year ago

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