A toy rocket is launched with vi=15 m/s at 50° above the horizontal. Fina the horizontal displacement, maximum height, and time of flight.

I will be happy to critique your thinking.

Think about doing the problem in reverse order. The vertical component of velocity determines the time of flight, which is twice the time it takes to decelerate to zero upward velocity, Vi sin 15/g. That is also the time of maximum height.