Question

Two swimmers A and B, of weight 190 lb and 125 lb, respectively, are at diagonally opposite corners of a floating raft when they realize that the raft has broken away from its anchor. Swimmer A immediately starts walking toward B at a speed of 2 ft/s relative to the raft. Knowing that the raft weighs 300 lb, determine (a) the speed of the raft if B does not move, (b) the speed with which B must walk toward A if the raft is not to move.

Answer 1

Answer:

a) 0.618 ft/s

b) 3.04 ft/s

Explanation:

Givens:

Weight of swimmer A $W_{A}$ = 190 Ib.

Weight of swimmer B  $W_{B}$= 125 Ib.

Weight of the raft $W_{R}$ = 300 Ib.  

Swimmer A walks toward swimmer B relative to the raft with a speed

$V_{A/R}$= 2 ft/s

a) Conservation of linear momentum

$m_{A} v_{A} +m_{B} v_{B} +m_{R} v_{R} =0..........(1)\\v_{A/R}=v_{A} -v_{R}\\\v_{A}=v_{A/R}+v_{R}.................(2)$

Since swimmer B does not move  

$v_{B} =v_{R}...............(3)$

Substitute from (2) and (3) into (1)

$m_{A} (v_{A/R} +v_{R} )+m_{B} v_{R} +m_{R} v_{R}=0\\(m_{A}+m_{B}+m_{R})v_{R} =-m_{A}v_{A/R}\\v_{R}=\frac{-m_{A}v_{A/R}}{m_{A}+m_{B}+m_{R}} \\v_{R}=0.618ft/s$

b) if the raft not to move $v_{R}=0$

from (2)

$v_{A} =v_{A/R}$

substitute in (1)

$m_{A} v_{A/R} +m_{B} v_{B}+m_{R} (0)=0\\v_{B}=\frac{W_{A}v_{A/R}}{W_{B}} \\v_{B}=3.04ft/s$