Kinematics – Projectile

1. The problem statement, all variables and given/known data

A stone is thrown with a velocity [itex]v_{0}[/itex] at an angle [itex]\alpha[/itex] to the horizontal (see image) from a step of height H. Calculate the x coordinate [itex]x_{1}[/itex] of the point where the stone hits the ground.

2. Relevant equations

[itex]x(t) = u_{x}t + x_{0}[/itex]
[itex]y(t) = u_{y}t + \frac{1}{2}at^{2} + y_{0}[/itex]

3. The attempt at a solution

[itex]u_{x} = v_{0}cos(\alpha)[/itex]
[itex]u_{y} = -v_{0}sin(\alpha)[/itex]

[itex]x_{1} = u_{x}t_{1}[/itex]
[itex]x_{1} = v_{0}cos(\alpha)t_{1}[/itex]
[itex]y(t) = 0 @ t_{1}[/itex]
[itex]0 = -v_{0}sin(\alpha)t_{1} – \frac{g}{2}(t_{1})^2 + H[/itex]

Here is where I have a discrepency with the provided (Bare Bones) Solution.

According to the solution; [itex]0 = v_{0}sin(\alpha)t_{1} – \frac{g}{2}(t_{1})^2 + H[/itex]

This seems to be missing the "-" in front of the 0 = [itex]v_{0}sin(\alpha)t_{1}[/itex] term.

My question is am I correct?

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