The Displacement of a Raft

Example 3 The Displacement of a Raft

At the moment that the forces

and

begin acting on the raft in Example 2, the velocity of the raft is 0.15 m/s, in a direction due east (the +x direction). Assuming that the forces are maintained for 65 s, find the x and y components of the raft's displacement during this time interval.

Reasoning Once the net force acting on an object and the object's mass have been used in Newton's second law to determine the acceleration, it becomes possible to use the equations of kinematics to describe the resulting motion. We know from Example 2 that the acceleration components are a_x = +0.018 m/s² and a_y = +0.011 m/s², and it is given here that the initial velocity components are v_0x = +0.15 m/s and v_0y = 0 m/s. Thus, Equation 3.5a

and Equation 3.5b

can be used with t = 65 s to determine the x and y components of the raft's displacement.

Solution According to Equations 3.5a and 3.5b, the x and y components of the displacement are

Figure 4.6d shows the final location of the raft.