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#17 on the MC Midterm review. We believe it to be 16 times greater not 8.
Yes, you are correct, number 17 is 16 times greater, thank you! The answer key has been revised.
Can someone please explain how to find the answer to #15, 17, and 20 on the midterm multiple choice review. Thank you.
Heather, here you go:
#15. Use the Second Kinematics Equation. Initial velocity is zero. so the equation becomes Delta y = 1/2at^2. Solve this for t and you find that t is proportional to the square root of delta y. So the package that is dropped from a height of 4H takes 2 times as much time to hit the ground as the package at height h. Answer B.
#17. Use the Third Kinematics Equation (there is no time in the problem). The final velocity at the max height is zero, so the equation, solved for delta y is: delta y = (v initial)^2/2a. The max height depends on the square of the initial velocity - so the arrow fired at 4 times the initial velocity of the other one rises to a height 16 times that one. Answer D.
#20. Use the second kinematics equation with the initial velocity and position equal to zero. Solve it for a.
a = 2x/t^2. Plug in the position and time at any of the points and you get a = 4 m/s^2. If you take the last point where x = 50 and t = 5 you get: a = 2(50)/5^2 = 4. Answer C.