Question

A 5-lb. force acting in the direction of (5,-3) moves an object just over 12 ft. from point (0,6) to (7,-4). Find the work done to move the object to the nearest foot-pound.
a. 11 ft * lbs
b. 34 ft * lbs
c. 56 ft * lbs
d. 61 ft * lbs

please show steps so I can learn!

Answer 1

Magnitude of force= |F|= 5 lb
In the direction of vector,let say M=5i-3j
As, we know that vector consists of magnitude and direction( unit vector)
                                        F=|F| M(unit vector).........1
In order to find the unit vector, divide the vector M by its magnitude.
M(unit vector)=(5i-3j)/√34
Now, the eq. 1 becomes
                                        F=5(5i-3j)/√34
                                        F=(25i-15j)/√34
As, the object moves from point let say P=0i+6j to Q=7i-4j
so,
                                   PQ=Q-P 
                                        =(7-0)i+(-4-6)j
                                        =7i - 10j
So,
                                  W= F.PQ
                                      =((25i-15j)/√34).(7i-10j)
                                      =(7*25/√34)+(-10*-15/√34)
                                      =55.7 lb*ft
                                      =56 lb*ft
Option C is correct