Unformatted text preview: r
, which happens at the time satisfying is 32 ft/s2. The ball will Solving for using the quadratic formula gives two times, one positive and one negative.
Only the positive time is physical. Therefore the solution is
s. At this time, the
velocity of the ball is
( 8 pts ) (  ) 7. We need to solve the Torricelli DE
()
At height the area is () √ () () . Thus the DE becomes Integrating: Using the fact that ( ) . Using ( ) gives then gives The tank is empty when
, which occurs at a time satisfying
hours (1 hour and 20 minutes)
8 pts 8. The cooling DE is
( ) Solving the DE

Using ( )
Using ( enables solution for the constant
) enables solution for the constant
() The milk will reach 5°C at a time satisfying
() (⁄)
(⁄) . Thus , i.e. when...
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 Fall '08
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