Question

A forceF has magnitude of 15N. Direction of F is at 37^(@) from nagative x-axis towards posititve y-axis. Represent F in terms of hat i and hat J .

Answer 1

Given:

Force  F  magnitude = 15N

direction - 37$\degree$^o

To find:

F in terms of i and j.( vector form)

solution :

Component of force in x axis =  |F|cos37

Component of force in y axis = |F|sin37

|F | is magnitude of force = 15

Force in x axis = -15cos37 = -11.97 N

Force in y axis = 15sin37 =  9.03N

F in vector form = -11.97i + 9.03j

Answer 2

Answer:

Given :

• Force = 15 N
• Direction of F : 37° (Towards the positive Y axis and away from negative X axis)

To show :

• Represent F in î and j.

Solution :

F_x = F cos 37°

So, F_x = 15 × 4/5

Hence, F_x = 12 N

Now, F_y = F sin 37°

So, F_y = 15 × 3/5

Hence, F_y = 9 N

Now, we know that, F = F_x (-i) + F_y (j)

⇒ F = (-12i + 9 j) N

Hence, the representation of the given force in the vectors is : (-12i + 9 j) N.