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Vertical Motion ProblemsText Box: Xiomara wants to figure out how much time it takes her ball to hit the ground if she launches it at a velocity of –45 ft/sec from a height of 60 ft. But when she was ready to throw the ball ,it falls from her hands. How long would it have taken if she threw the ball instead of dropping it ,and How much time did it actually take the ball to hit the ground when it was dropped?  

 

 

 

 

 

 

 

 

 

 

Thrown Problem

Dropped Problem

 

 

H= 0          h=-16t2+vt+s

V= -45      0=-16 t2-45t+60

T= t           t=-b±√b2-4ac

S= 60                   2a

                  t= -(-45) ±√-452-4(-16)(60)

                                    2(-16)

                  t= 45±√2025+3840

                                 -32

                  t= 45±√5865

                           -32

                  t= 45±76.58

                           -32

                  t= 121.58   or  t= -31.58

                         -32                   -32

                  t= -3.80           t= 0.99 sec

 

  H= 0           h= -16t2+s

  T= t            0= -16t2+60

  S= 60         -60          -60

                   -60= -16 t2

                              -16   -16

                  √3.75=√t2

                           ±1.94 sec=t