Answer:
16275 Joule
Explanation:
Work Done By A Constant Force
The work can be computed as
W=F.X, where F is the applied force (in this case, the force needed to overcome gravity)
Recall the second Newton's law which states that
[tex]F_n=m.a[/tex]
Being [tex]F_n[/tex] the net force on a system of mass m and acceleration a
We know the helicopter is applying force against gravity because the speed of the shipwreck survivor changes from 4 m/s to 0 m/s in 15 meters
Let's calculate that acceleration by using the dynamics equation
[tex]V_f^2=V_o^2+2aX[/tex]
Solving for a
[tex]\displaystyle a=\frac{V_f^2-V_o^2 }{2X}[/tex]
a=-0.533\ m/sec^2
The negative sign indicates the body is braking, we'll later use the magnitude
The net force is, then
[tex]F_n=(105\ kg)(0.533\ m/sec^2)[/tex]
[tex]F_n=56\ Nw[/tex]
The only two forces acting upon the survivor is the lifting force of the helicopter and the weight of the man, so
[tex]F_h-W=56\ Nw[/tex]
[tex]F_h=mg+56\ Nw=105\ kg\ 9.8\ m/sec^2+56\ Nw[/tex]
[tex]F_h=1085\ Nw[/tex]
Finally, the work done by the helicopter is
[tex]W=(1085\ Nw)(15\ m)=16275 \Joule[/tex]
The work done by the helicopter is
[tex]\boxed{16275\ Joule}[/tex]
