Jeff tosses a can of soda pop to Karen, who is standing on her 3rd floor balcony a distance of 8.5m above Jeff’s hand. Jeff gives the can an initial velocity of 16m/s, fast enough so that the can goes up past Karen, who catches the can on its way down. Calculate the velocity of the can the instant before Karen grabs the can. How long after Jeff tosses the can does Karen have to prepare to catch it?

Question

Jeff tosses a can of soda pop to Karen, who is standing on her 3rd floor balcony a distance of 8.5m above Jeff’s hand.  Jeff gives the can an initial velocity of 16m/s, fast enough so that the can goes up past Karen, who catches the can on its way down.  Calculate the velocity of the can the instant before Karen grabs the can.  How long after Jeff tosses the can does Karen have to prepare to catch it?

Henry · Answer

V^2 = Vo^2 + 2g*h.
V^2 = 16^2 - 19.6*8.5 = 89.4
V = 9.46 m/s = The velocity when it reaches the balcony and when it returns to the balcony and grabbed by Karen.

V = Vo + g*Tr = 0.
16 - 9.8Tr = 0
Tr = 1.63 s. = Rise time from Jeff's hand to max ht.

V = Vo + g*Tf = 9.46.
0 + 9.8Tf = 9.46
Tf = 0.965 s. = Fall time from max ht. to balcony where Karen grabs it.

Tr+Tf = 1.63 + 0.965 = 4.23 s. = Time in air = Time Karen have to prepare to catch it.