Particle Launched over 13.7m Gorge - Speed & Angle Calculation

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The discussion focuses on calculating the launch speed of a particle projected over a 13.7 m gorge at a 14° angle, landing with 1.7 m to spare. The initial calculation suggested a speed of 16 m/s, but it was pointed out that gravity must be factored into the equation, as it affects projectile motion. The conversation also touches on how launch speed varies based on gravitational forces on different celestial bodies. Additionally, there is a query about determining the launch angle if the particle falls 0.5 m short when launched at a different angle. The participants emphasize the importance of including gravitational acceleration in their calculations for accurate results.
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A particle is launched over a gorge that is 13.7 m straight across and 100 m deep. The particle is launched at an angle of 14° above the horizontal, and lands with 1.7 m to spare.
What was the particle's launch speed?
If the particle was launched at a different angle, but fell 0.5m short, what would it's launch angle be?

For the first part, I figured that the launch speed should be x, where x*cos(14 deg) = 15.4 m, so x = 16 m/s, but this is not correct. Why?
 
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I got a different answer. Your answer is wrong because gravity affects the answer and you have no g in yours. On the moon a smaller speed would suffice, while on Jupiter a very large velocity is needed.

Show your work and someone will be very happy to sort it out!
 
I realized what I was doing wrong. Thanks for the tip.
 

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