Two forces, given by F1 = (-6.00i - 4.00j) N and F2 = (-3.00i + 7.00j) N, act on a particle of mass 2.00

kg that is initially at rest at coordinates (-2.00 m, 4.00 m). (a) What are the components of the particle’s

velocity at t = 10.0 s? (b) In what direction is the particle moving at t = 10.0 s? (c) What displacement

does the particle undergo during the first 10.0 s? (d) What are the coordinates of the particle at t = 10.0

s?

In[2104]:= eqs = 8SumFx � F1x + F2x,

SumFx � m * ax,

SumFy � F1y + F2y,

SumFy � m * ay,

vxf � vxi + ax * t,

vyf � vyi + ay * t,

xf � xi + vxi * t + 1 � 2 * ax * t^2,

yf � yi + vyi * t + 1 � 2 * ay * t^2,

m ¹ 0,

vxi � 0,

vyi � 0,

t ¹ 0, SumFy ¹ 0, SumFx ¹ 0

<;

vals = 8xi ® -2, yi ® 4, F1x ® -6, F2x ® -3, F1y ® -4, F2y ® 7, t ® 10, m ® 2<;

What are the components of the particle’s velocity at t

= 10.0 s?

In[2106]:= Reduce@eqs, 8vxf, ax, SumFx<D;

Cases@%, Hvxf � _LD% �. vals

Out[2107]= :vxf �

HF1x + F2xL t

m

>Out[2108]= 8vxf � -45<In[2109]:= Reduce@eqs, 8vyf, ay, SumFy<D;

Cases@%, vyf � _D% �. vals

Out[2110]= :vyf �

HF1y + F2yL t

m

>Out[2111]= 8vyf � 15<

In what direction is the particle moving at t = 10.0 s?

In[2112]:= Reduce@Append@eqs, Tan@vfAngleD � vyf � vxfD, 8vfAngle, ax<D;

Cases@%, vfAngle � _D;

% �. 8C@1D ® 1<% �. vals �� N;

%@@1, 2DD � °

Out[2114]= :vfAngle � Π + ArcTanB F1y + F2y

F1x + F2x

F>Out[2116]= 161.565

What displacement does the particle undergo during

the first 10.0 s?

In[2139]:= Join@eqs, 8Dx � xf - xi, Dy � yf - yi, displacement^2 � Dx^2 + Dy^2<D;

Reduce@%, 8displacement, Dx, Dy, xf, yf, vxf, vyf, ax, SumFx, SumFy<D

Out[2140]= vyi � 0 && vxi � 0 && m ¹ 0 && ay �

F1y + F2y

m

&&

displacement � -

F1x2

+ F1y2

+ 2 F1x F2x + F2x2

+ 2 F1y F2y + F2y2

t2

2 m

ÈÈ

displacement �

F1x2

+ F1y2

+ 2 F1x F2x + F2x2

+ 2 F1y F2y + F2y2

t2

2 m

&&

F1y + F2y ¹ 0 && Dx �

ay HF1x + F2xL t2

2 HF1y + F2yL && Dy �

ay t2

2

&& xf � xi + Dx &&

yf �

1

2

Iay t2

+ 2 yiM && vxf �

ay F1x t + ay F2x t

F1y + F2y

&& vyf � ay t &&

ax �

ay F1x + ay F2x

F1y + F2y

&& SumFx � F1x + F2x && SumFy � F1y + F2y && F1x t + F2x t ¹ 0

In[2156]:= displacement �

F1x2+ F1y2

+ 2 F1x F2x + F2x2+ 2 F1y F2y + F2y2 t2

2 m�. vals;

% �� N

Out[2157]= displacement � 237.171

2 PSE PE PROBLEM 5.60.nb

What are the coordinates of the particle at t = 10.0 s?

In[2121]:= Reduce@eqs, 8xf, vxf, ax, SumFx<D;

Cases@%, xf � _D% �. vals

Out[2122]= :xf �

F1x t2+ F2x t2

+ 2 m xi

2 m

>Out[2123]= 8xf � -227<In[2133]:= Reduce@eqs, 8yf, vyf, ay, SumFy<D;

Cases@%, yf � _D% �. vals

Out[2134]= :yf �

F1y t2+ F2y t2

+ 2 m yi

2 m

>Out[2135]= 8yf � 79<

PSE PE PROBLEM 5.60.nb 3