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## Projectile Motion Examples

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### Title: Lecture 4a Subject: Chapter 4: Part II: Projectile Motion Examples Author: Charles W. Myles Last modified by: Charles Myles Created Date: 8/11/2000 3:05:01 PM – PowerPoint PPT presentation

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Title: Projectile Motion Examples

1
Projectile Motion Examples
2
Example 4.3 The Long Jump
Problem A long-jumper (Fig. 4.12) leaves the
ground at an angle ?i 20 above the horizontal
at a speed of vi 8.0 m/s. a) How far does
he jump in the horizontal direction?
(Assume his motion is equivalent to that of a
particle.) b) What is the maximum height
reached?
3
Example Driving off a cliff!!
• y is positive upward, yi 0 at top. Also vyi
0
• How fast must the motorcycle leave the cliff to
land at
• xf 90 m, yf -50 m? vxi ?

vx vxi ? vy -gt x vxit, y - (½)gt2 Time
to Bottom t v2yf/(-g) 3.19 s vxi (xf/t)
28.2 m/s
4
Kicked football
• ?i 37º, vi 20 m/s
• ? vxi vicos(?i) 16 m/s, vyi visin(?i) 12
m/s
• a. Max height? b. Time when hits ground?
• c. Total distance traveled in the x direction?
• d. Velocity at top? e. Acceleration at top?

vf
vyi
vxi
5
Conceptual Example
vyi
• Demonstration!!

vxi
vyi
vi
vxi ?
6
Conceptual Example Wrong Strategy
• Shooting the Monkey!!
• Demonstration!!

vi ?
7
Example
• Range (R) of projectile ? Maximum horizontal
distance before returning to ground. Derive a
formula for R.

xi 0 yi 0

?i

?i
?i1
?i1
?i2
8
• Range R ? the x where y 0!
• Use vxf vxi , xf vxi t , vyf
vyi - gt
• yf vyi t (½)g t2, (vyf) 2
(vyi)2 - 2gyf
• First, find the time t when y 0
• 0 vyi t - (½)g t2
• ? t 0 (of course!) and t (2vyi)/g
• Put this t in the x formula xf vxi (2vyi)/g
? R
• R 2(vxivyi)/g, vxi vicos(?i), vyi visin(?i)
• R (vi)2 2 sin(?i)cos(?i)/g
• R (vi)2 sin(2?i)/g (by a trig identity)

9
Example 4.5 Thats Quite an Arm!
Problem A stone is thrown from the top of a
building at an angle ?i 26 to the horizontal
and with an initial speed vi 17.9 m/s, as in
Fig. 4.14. The height of the building is 45.0
m. a) How long is the stone "in
flight"? b) What is the speed of the
stone just before it strikes the
ground?
10
Example A punt!
• vi 20 m/s, ?i 37º
• vxi vicos(?i) 16 m/s, vyi visin(?i) 12 m/s

11
Proof that projectile path is a parabola
• xf vxi t , yf vyi t (½)g t2
• Note The same time t enters both equations!
• ? Eliminate t to get y as a function of x.
• Solve x equation for t t xf/vxi
• Get yf vyi (xf/vxi) (½)g (xf/vxi)2
• Or yf (vyi /vxi)xf - (½)g/(vxi)2(xf)2
• Of the form yf Axf B(xf)2
• A parabola in the x-y plane!!

12
Problem
vi 65 m/s
65
13
Example 4.6 The Stranded Explorers
Problem An Alaskan rescue plane drops a package
of emergency rations to a stranded party of
explorers, as shown in the picture. If the plane
is traveling horizontally at vi 42.0 m/s at a
height h 106 m above the ground, where does the
package strike the ground relative to the point
at which it is released?
vi 65 m/s
h