SOLUTION: The final velocity v of an object in feet per second (noted aa ft/sec) after it slides down a frictionless inclined plane of height h feet is given by v = sqrt{64h + (v_0)^2},

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Question 1208652: The final velocity v of an object in feet per second (noted aa ft/sec) after it slides down a frictionless inclined plane of height h feet is given by

v = sqrt{64h + (v_0)^2}, where v_0 is the initial velocity (in ft/sec) of the object.

A. Solve the given formula for h.

B. What is the final velocity v of an object that slides down a frictionless inclined plane of height 4 feet? Assume that the initial velocity is 0.
Answer by Shin123(626) About Me  (Show Source):
You can put this solution on YOUR website!
a)
Since the h is hard to work with when it's inside a square root, we square both sides to get v%5E2=64h%2B%28v_0%29%5E2. Subtracting %28v_0%29%5E2 from both sides gives 64h=v%5E2-%28v_0%29%5E2. Finally, dividing both sides by 64 gives h=%28v%5E2-%28v_0%29%5E2%29%2F64.
b)
Going back to the original formula, we see that we have to plug in h=4 and v_0=0 from the problem statement. Doing so gives v=sqrt%2864%2A4%2B0%5E2%29=sqrt%28256%29=16, so the final velocity is 16 ft/sec.