word problem

Question

You drop a pencil out a window that is 20 ft above the ground. Use the formula V² = 64s, where V is the distance fallen, to calculate the speed the pencil is traveling when it hits the ground.

Answer 1

The problem statement incorrectly calls v the distance (as Walter pointed out).  It should call v the final speed attained at the bottom of the fall, and s is the distance fallen.  The correct formula to use is the kinematic relationship

 

v² = 2gs

 

where

 

v = speed at bottom in ft/sec

g = acceleration of gravity = 32 ft/sec², which makes 2g = 64 ft/sec²

s = distance fallen = 20 feet

 

Then

 

v = √(2gs) = √(64 x 20) ft/sec ≅ 35.78 ft/sec

Answer 2

[Note: I think it's odd to use "V" for "distance".  Most physics uses "v" for "velocity" (like speed, but with direction), and "d" is for "distance" (or displacement).]

 

Anyway, as for your question...

 

Simply substitute and solve for s.

 

V²=64s

(20)²=64s

 

Follow the order of operations.  Resolve exponents.  Then divide to isolate s.  I'm pretty sure you can do that.