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- Homework Statement
- A projectile reaches a maximum height of 14.5 meters and travels a horizontal distance of 52.6 meters. How long was it in the air?

- Relevant Equations
- Vfy = V0y - 9.8t

I've been trying some online projectile problems. Specifically, I was using this one on master difficulty, looking at row e. It uses a random number generator; I shared the data I received in the Homework Statement above.

According to the help section, you can solve this with the formula given, but I don't see how. In fact, they seem to suggest that you don't even need the horizontal displacement, and can figure out the flight time of a projectile with just its maximum height, but there are lots of combinations of angles and velocity that will produce the same maximum height with different flight times.

I sort of cheated my way into a solution using this calculator. Note the calculator can't solve for time with just the two pieces of data given. What I did was put in horizontal distance (and initial height of 0) and start guessing at times until I found that 3.44 seconds produces a height of 14.5 meters.

Can anyone explain to me the correct approach to solving this problem?

According to the help section, you can solve this with the formula given, but I don't see how. In fact, they seem to suggest that you don't even need the horizontal displacement, and can figure out the flight time of a projectile with just its maximum height, but there are lots of combinations of angles and velocity that will produce the same maximum height with different flight times.

I sort of cheated my way into a solution using this calculator. Note the calculator can't solve for time with just the two pieces of data given. What I did was put in horizontal distance (and initial height of 0) and start guessing at times until I found that 3.44 seconds produces a height of 14.5 meters.

Can anyone explain to me the correct approach to solving this problem?