Formula Sheet for Test 2

Ideal Projectile Motion Equation from the

origin

jir

2

002

1)sin(cos gttvtv

Maximum height

g

vy

2

sin2

0

max

Flight time

g

vt

sin2 0

Range

2sin

2

0

g

vR

General Projectile Motion Equation

jir

2

00002

1)sin()cos( gttvytvx

Arc Length Formula

dtdtdt

dz

dt

dy

dt

dxL

b

a

b

a

v

222

Speed on Smooth Curve

)(tdt

dsv

Unit Tangent Vector

v

vT

Principal Unit Normal Vector

dtd

dtd

/

/

T

TN

Binormal Vector

NTB

Curvature

3

1 v aT T

v v

d d

ds dt

Torsion

2

.

av

NB

. . .. . .. . .

. .. .. .

..

zyx

zyx

zyx

ds

d

Tangential and Normal Scalar Components of

Acceleration

NTa NT aa

where vdt

daT

222

TN aa av