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So x is v0 cos θ times t.
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And y is v0 sin θ times t minus one half times g t square.
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Now we know everything about this particle.
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I told you once you know the free parameters, R0 and v0,
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you know everything about the future of the object.
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Let's ask, what's the range? Range is that distance.
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What's the strategy for range?
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You see how long you are in the air
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and the whole time you are in the air,
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you are traveling horizontally at this speed.
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Again, let t* be the time when you hit the ground.
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You said 0 = ( v0 sin θ -1/2 g t*^2) t*.