Projectile Motion 1

Projectile Motion:Speed

Scott Starks, PhD, PEDept. of Electrical & Computer Engineering

UTEP

Projectile Motion 2

At time t=0, an artillery shell is launched with a vertical speed of v0 from atop a fortress that is situated atop a mountain of height y0.

Example: Artillery Shell

y000

2

2

1ytvtgy

Projectile Motion 3

y is the height (ft) of the projectile above the ground at time t (s)

g is the acceleration constant (32 ft/s2) v0 is the muzzle (initial) velocity (ft/s) y0 is the height of the cannon above ground (ft)

Note: We are only considering vertical height in this example.

Equation of Motion (Vertical)

002

2

1ytvtgy

Projectile Motion 4

Assume the cannon is located 672 ft above ground level.

Assume the muzzle velocity is 656 ft/s.

Initial Conditions

)(6720 fty

)/(6560 sftv

Projectile Motion 5

Incorporate Initial Conditions in Equation of Motion

)(67265616

672)656()32(2

12

1

2

2

002

fttty

tty

ytvtgy

Projectile Motion 6

Height of the Projectile (y)

Table Plot

t (s) y (ft)0 6721 13122 19203 24964 30405 35526 40327 44808 48969 5280

10 563211 595212 624013 649614 672015 691216 707217 720018 729619 736020 739221 7392

22 736023 729624 720025 707226 691227 672028 649629 624030 595231 563232 528033 489634 448035 403236 355237 304038 249639 192040 131241 67242 0

0 5 10 15 20 25 30 35 40 450

1000

2000

3000

4000

5000

6000

7000

8000

y (ft)

t (s)

Projectile Motion 7

The vertical speed (v) of the projectile measured in (ft/s) at time (t) is described by the equation

Vertical Velocity (Speed) of the Projectile

)/(65632

32 0

sfttv

vtv

Projectile Motion 8

Vertical Velocity (Speed) of the Projectile

Table Plot

t (s) v (ft/s)0 6561 6242 5923 5604 5285 4966 4647 4328 4009 368

10 33611 30412 27213 24014 20815 17616 14417 11218 8019 4820 1621 -16

22 -4823 -8024 -11225 -14426 -17627 -20828 -24029 -27230 -30431 -33632 -36833 -40034 -43235 -46436 -49637 -52838 -56039 -59240 -62441 -65642 -688

t (s)0 5 10 15 20 25 30 35 40 45

-800

-600

-400

-200

0

200

400

600

800

v (ft/s)