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The perspective provided by Multiple-Concept Example 9 is useful here. The highest barrier that a projectile can clear is 13.5 m, when the projectile is launched at an angle of 15.0 above the horizontal. What is the projectile’s launch speed?

62.8$m / s$

Physics 101 Mechanics

Chapter 3

Kinematics in Two Dimensions

Motion in 2d or 3d

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so the question states that a projectile is launched at 15 degrees and the highest barrier it can go over is 13.5 meters high. And so we need to try and find what this velocity V is equal to so that it goes over at its maximum point. Um so it's maximum point is 13.5 meters high. So to do this, we first can separate our velocity into two components. In this case, we just need to focus on the vertical component of the velocity which we confined because we no sign of 15 degrees is equal to the opposite overhype. On news that the opposite in this case is the vertical come on component of the velocity over the high pot news which is just the philosophy, which means that the vertical component is equal to V time sign of 15 degrees. And now that we know this, we can use our kingdom Alex Equation, which states that the final velocity squared is equal to the initial velocity squared plus two times the acceleration times, the displacement. So we know when the project owes at its maximum, it's vertical velocity will be zero. We know what the initial vertical velocity is of the protector, which is the sign 15 degrees so b squared. And we know that the acceleration is going to be nine negative, 9.8 meters per second squared due to gravity, and we know the displacement will be 13.5 meters. Now. All we have to do is sell for V, so consider tracked this on both sides, so it's attract negative to iris. Attract two times negative, 9.8 times 13.5 on both sides. I give you this, then we can take the square root on both sides. We get square root of two times 98 times 13.5 is equal to be signed 15 degrees and divide by sign of 15 degrees on both sides. That means V is equal to square root of two times 9.8 times 13.5 divided by sine of 15 degrees, which is the same thing as 62 0.8 meters per second

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