Given...

Cannon on ground, firing at angle theta, creates parabola. Assume physicists' world — no air friction, flat ground, -9.8m/s gravity, etc.

• An angle of firing: theta
• Gravity: -9.8m/s
• Velocity of Cannon: v_0

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How does a lovely physicist do trig?

How can we calculate time of impact?

Reminder: all vectors (v) is just the sum of two components v_x and v_y.

We know that any 2D vector of velocity is just the combination of its x & y component, we could use this...

...surprisingly lovely right triangle & a touch of trig to see that...

$$ sin(\theta)=\frac{{v_0}_y}{v_0} $$

Which, leads us to find that

$$ sin(\theta)*{v_0}={v_0}_y $$

Great! We now are reduced to a one-dimensional motion problem — finding (t) with respect to v_0_y. Very nicely, we now have the following problem: