A particle undergoes three successive displacements in a plane, as follows: d^ri

Question

A particle undergoes three successive displacements in a plane, as follows: d^rightarrow_1, 6.83 m southwest; then d^rightarrow_2, 2.63 m east; and finally d^rightarrow_3, 1.29 m in a direction 69.4 degree north of east. Choose a coordinate system with the y axis pointing north and the x axis pointing east. What are the x component and the y component of d^rightarrow_1? What are the x component and the y component of d^rightarrow_2 ? What are the x component and the y component of d^rightarrow_3? What are the x component, the y component, and the magnitude of the particle's net displacement? the direction of the net displacement? If the particle is to return directly to the starting point, how far should it move?

Explanation / Answer

Ans:-

Let's break up the three displacements into (x,y) values.
Southwest would be 225 degrees
a]x=6.83 cos 225=-4.829 m
b] y=6.83 sin 225=-4.829m
East is 0 degrees
c] x=2.63 cos 0=2.63m
d] y=2.63 sin 0=0
69.4 degrees north of east would be 69.4 degrees,
e]x=1.29 cos(69.4)=0.454m
f]y=1.29 sin(69.4)=1.21 m
Now tally up all of the x's and y's.
Assume the particle started at (0,0)
x=-4.829+2.63+0.454=-1.745
y=-4.829+0+1.21=-3.619
The magnitude would be
sqrt(x^2+y^2)

=sqrt(-1.745^2+-3.619^2) = 4.02m

The direction is
tan(A)=-3.619/-1.745
A=64.3 degrees North of East

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.