Finding the range for projectile motion from a cliff

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This is pretty much the hardest projectile motion problem you will see. If you can solve this, you should be OK.

Here a ball is on a cliff 12 meters high and launched with a velocity of 5 m/s at a 30 degree angle. How far from the base of the cliff will the ball land?
  1. Dot Physics
  2. physics
  3. projectile motion
  4. kinematics
  5. mechanics
  6. launch
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Thank you so much, this really helped!

Stubwood_on_YT
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sure, why easy if you can do it difficult? instead of solving a linear x equation for t and substituting t in the quadratic y equation, let's solve the quadratic y equation for t and substitute the t in the linear x equation.

It, of course, turns out to be the same, however, I would always recommend our students to solve the linear equation for t and substitute the t in the quadratic equation. There is still a quadratic equation y = y(x) to solve, but at least they don't have to deal with squareroots and negative times in y(x).

Situations like 11:30 "am I doing this right?" would at least be avoided in the step where you try to eliminate t.

Edit: ok, you are not trying to eliminate t, you are solving for t and use the numerical value that you calculate and plug it into t. ok. just ignore my comment then because it doesn't apply.

compphysgeek