Question: A pellet gun is fired straight up from the edge of a cliff that is 20m

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Question: A pellet gun is fired straight up from the edge of a cliff that is 20m above the ground. The pellet returns to the cliff after 5.2 s. If the same pellet gun is fired straight downward from the edge of the cliff, with what velocity will it hit the ground?

--I have attempted to solve this, and after working through the steps I received an answer of 32.27 m/s for the velocity that the pellet will hit the ground. This was based on finding the initial velocity for the pellet gun as it fired upwards, with consideration of the time it took to reach its peak height which would be half of the total time of 5.2s in an ideal world without friction. This initial velocity was found to be 25.48 m/s upward. Therefore, shooting downward the initial velocity would be the same, over a distance of 20 m as given, and with the acceleration of -9.8m/s2 due to gravity. I then plugged into the equation Vf2= V0 + 2ax to find the final velocity. I am lacking a solution set for this practice test, and would really appreciate if someone could check this work to make sure I am understanding the problem correctly. THANK YOU!!

Explanation / Answer

Total time = 5.2 s so time for travel in one-direction = 5.2/2 = 2.6 sec

So height travelled abvoe the launching point = 0.5*9.8*2.6^2 = 33.124 m

so firing velocity = velocity at which it comes back to that point = sqrt(2*g*height) = 25.48 m/s^2

Shooting downward will give acceleration right from start.

So final velocity = sqrt(25.48^2 + 2*9.8*20) = 32.368 m/s

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