A raft of mass 180kg carries two swimmers mass of 50kg and 80kg. The raft is initially floating at rest. The two swimmers simultaneously dive off opposite ends of the raft each with a horizontal velocity of 3 m/s. With what velocity in in which direction does the raft start to move

Assuming swimmer 1 is at the left of the raft and swimmer 2 is at the right (as shown in the figure), we can make a Free body diagram and find in which direction is the greatest exerted horizontak force on the raft:

[tex]Fx_{net}=-F_{swimmer1}+F_{swimmer2}[/tex]

Where:

[tex]F_{swimmer1}=m_{1}g[/tex]

Being [tex]m_{1}=50 kg[/tex] the mass of swimmer 1 and [tex]g=9.8 m/s^{2}[/tex] the acceleration due gravity

[tex]F_{swimmer2}=m_{2}g[/tex]

Being [tex]m_{1}=80 kg[/tex] the mass of swimmer 2

Then:

[tex]F_{swimmer1}=(50 kg)(9.8 m/s^{2})490 N[/tex] (1)

[tex]F_{swimmer2}=(80 kg)(9.8 m/s^{2})=784 N[/tex] (2)

Comparing both forces, and taking into account each swimmer has a horizontal velocity of [tex]3 m/s[/tex], we can deduce the raft will move in the direction of the greatest force, which is where swimmer 2 is (to the right).