Zachary Weber
AP Physics
2.2.10
10/7/09

1. A)
Y=Y0+Vt+(1/2)at^2
Cos(70)=x/35
Sin(70)=x/35

V1= velocity of ball
V1x=35tcos(70)=11.9707t
V1y=35tsin(70)=32.8892t

V2= velocity of gravity
V2x= 0
V2y= -(1/2)9.8t^2

Combined equations
Vx=11.9707t
Vy=32.8892t - (1/2)9.8t^2

Y=32.8892t-(1/2)9.8t^2
6=32.8892t-(1/2)9.8t^2
0=-6+32.8892t-(1/2)9.8t^2
t=6.5244032
6.534403 seconds
B.)11.9707(6.5344)=78.2213Meters
C.) t=6.534403/2=3.2672seconds
32.8892(3.2672)-(1/2)9.8(3.2672)^2=68.4636 meters

2.)
V1= apple
V2=arrow

V1x=0
V1y=-(1/2)9.8t^2
V2y=-(1/2)9.8t^2
V2x=(-(1/2)9.8)^2+V2x^2=40^2
V2x=square root1575.99
V2x=39.6987

Combined vectors
Vy=-(1/2)9.8t^2
Vx=39.6987t

10/Vx=t
10/39.6987=.251897
time for arrow to reach meeting place, t=.251897seconds

1.5=20-(1/2)9.8t^2
-18.5=-(1/2)9.8t^2
37=9.8t^2
3.7755=t^2
time for apple to reach meeting place, t=1.94306459seconds
1.94306459-.251897=1.69116759 seconds

He should release the arrow 1.691167 seconds after the apple is dropped.

3.)A.)
V1=velocity of ball
V2= Velocity of gravity

V1y= sin(45)=x/22
V1y=15.55634
V1x=cos(45)=x/22
V1x=15.55634

V2x=0
V2y=-(1/2)9.8t^2

Combined
Vx=15.55634t
Vy=15.55634t-(1/2)9.8t^2

0=15.55634t-(1/2)9.8t^2
t=3.174763
15.55634(3.174763)=49.3877
49.3877-25=24.3877/3.174763=7.681745M/second

B.) 3.174763/2=1.5873815seonds
15.5563(1.5873815)-(1/2)9.8(1.5873815)^2=12.3468

4.) A.) V1=Plane
V2=wind
North=90degrees
East=0degrees
South=-90degrees
West=180degrees

V1y=Sin(-45)=x/200
V1y=-141.4213562
V1x=cos(-45)=x/200
V1x=141.4213562

V2y=sin45=x/60
V2y=42.426406
V2x=cos45=x/60
V2x=42.426406

Combined
Vx=141.4213562x+42.6406
Vx=186.8477631x
Vy=-141.4213562x+42.6406
Vy=-98.7807562x
Tanx=-98.7807562/186.8477631
X=-27.86405276 degrees
The plane will travel east-southeast

B.) -98.7807562^2+186.8477631^2=landspeed^2
211.3521336M/s=ground speed