SOLUTION: You drop a penny from a 70-foot high bridge. What is the velocity of the penny when it hits the water below? Neglect the effect of air resistance and round your answer to the nea
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Question 324529: You drop a penny from a 70-foot high bridge. What is the velocity of the penny when it hits the water below? Neglect the effect of air resistance and round your answer to the nearest unit.
Found 2 solutions by Alan3354, solver91311:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Find the time until impact.
s = (1/2)at^2
a = acceleration due to gravity, ~32 ft/sec/sec on Earth
70 = 16t^2
t^2 = 70/16 = 4.375
t = 2.09 seconds
-----------------
v = at = 32*2.09
v =~ 67 ft/sec
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
The height of an object in vertical motion near the earth's surface at time 
is given by:
\ =\ -16t^2\ +\ v_ot\ +\ h_o)
Where 
is the initial velocity (assumed to be zero for this problem since the penny was dropped, not thrown) and 
is the initial height, 70 feet in this case.
\ =\ -16t^2\ +\ 70)
We want to know the time when \ =\ 0)
We are ignoring the negative square root since it is unlikely that we will be able to make time go backwards.
The instantaneous velocity of a falling object at time is given by:
\ =\ -32t\ +\ v_o)
Clever calculus students will recognize this function as the first derivative of the height function.
All that is required is to calculate the velocity at the time calculated above, recalling that 
:
\ =\ -32\frac{\sqrt{70}}{4}\ =\ -8\sqrt{70})
You can push buttons on a calculator as well as I can. "But wait," you say, "why is the velocity negative?" Easy, the penny is going downward.
John
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