Answer:
a) F= 4 i + 4
j
b) Θ=11.3
c) The work done is 20
Step-by-step explanation:
a) ||F||=8, α=π/4
Fx=||F||·sin(π/4)=8·
Fy=||F||·cos(π/4)=8·
F=Fx i + Fy j = 4 i + 4
j
b) We can find the value of Θ using the equation:
cos(Θ)=
where:
D= 3 i + 2 j
F=4 i + 4
j
The dot product is defined as the sum of the products of the components of each vector as:
F · D=
||F||= 8
||D||=
Hence:
Θ=arccos()
Θ=arccos(0.981)
Θ= 11.3°
c) Work is equal to:
F · D= =28.3
Other way of obtainig the work is:
||F||||D||cos(Θ)
where:
||F||= 8
||D||=
Θ=11.3°
So, ||F||||D||cos(Θ)=8××cos(11.3°)=28.3