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Response Details:
By knowing the mass and initial KE, we can find the initial velocity:
set up the equations of motion:
 , constant acceleration due to gravity
 , velocity is the integral of acceleration
 , position is the integral of velocity
 , constant velocity in the x-direction
 , position is the integral of velocity
at the highest point, the y-velocity is zero. so we first need to find the time at which that occurs:
now we answer the questions:
Part A)
Part B)
Part C)
65m/s is faster than the initial launch speed, so it must be below the launch point. Solving for velocity here will get you a negative answer for the time, which is alright for the problem. The projectile has already passed its highest point and is on its way down, but you can't find that time starting from this condition. The time it gives you is if the projectile was launched from a lower height with a higher initial velocity (such that it is at 52.4 m/s when it reaches the original height). But you can solve through all of the equations and it gives you the correct location. you just need to remember that you can't use this to find the correct location of the projectile:
so the projectile is 75.7 meters below the initial launch point
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