Optimal Angle and Horizontal Range of a Bottle Rocket Projectile

[EmmaB03]

Homework Statement

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A bottle rocket can shoot its projectile vertically to a height of 26.0m. At what angle should the bottle rocket be fired to reach its maximum horizontal range, and what is that range? (You can ignore air resistance).

Homework Equations

The Attempt at a Solution

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For the first part: I think the angle the rocket should be fired is 45 degrees, because it's the optimal angle for projectiles, where it travels the furthest when launched at this angle; am I right?

For the second part: I have no idea what to do to start this part of the problem. I know that I now have the angle (45) and the height (26.0). I don't know where to go from this point.

 

[MarkFL]

I would begin with (and orienting our coordinate axes such that the initial position is at the origin $\left(x_0,y_0\right)=(0,0)$):

$x(t)=v_0\cos(\theta)t\tag{1}$

$y(t)=-\dfrac{1}{2}gt^2+v_0\sin(\theta)t\tag{2}$

Solve (1) for $t$, and substitute into (2)...what do you get?