HP 48gII Graphing, 50g Graphing manual Linear Motion 8, Object in Free Fall 8, Projectile Motion 8

Linear Motion (8, 1)

Equations:

x = x0 + v0 ⋅		1	⋅ a ⋅ t	2
		t + --
		2
x = x0 +	1	⋅ (v0 + v) ⋅ t
	--
	2

1	⋅ a ⋅ t	2
x = x0 + v ⋅ t + --
2

v = v0 + a ⋅ t

Example:

Given: x0=0_m, x=100_m, t=10_s, v0=1_m/s

Solution: v=19_m/s, a=1.8_m/s^2.

Object in Free Fall (8, 2)

Equations:

1	⋅ g ⋅ t	2
y = y0 + v0 ⋅ t + --
2

v2 = v02 + 2 ⋅ g ⋅ (y + y0)

1	⋅ g ⋅ t	2
y = y0 + v ⋅ t + --
2

v = v0 + g ⋅ t

Example:

Given: y0=1000_ft, y=0_ft, v0=0_ft/s

Solution: t=7.8843_s, v= 253.6991_ft/s.

Projectile Motion (8, 3)

Equations:

x = x0 + v0 ⋅ COS( θ 0) ⋅ t		y = y 0 + v0 ⋅ SIN(θ 0) ⋅ t –	1	⋅ g ⋅ t2
			2
vx = v0 ⋅ COS(θ 0)		vy = v0 ⋅ S IN(θ 0) – g ⋅ t
R =	v02	⋅ S IN(2 ⋅ θ 0)
	g

Example:

Given: x0=0_ft, y0=0_ft, Θ 0 =45_°, v0=200_ft/s, t=10_s.

Solution: R=1243.2399_ft, vx=141.4214_ft/s, vy= 180.3186_ft/s, x=1414.2136_ft, y= 194.4864_ft.

Equation Reference 535