motion in two dimensions projectiles. under the influence of gravity alone, near the earths surface...
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Motion in Two Dimensions
Projectiles
Projectiles
• Under the influence of gravity alone, near the Earth’s surface an object accelerates downward at 9.8 m/s2.
• This acceleration is vertical and does not affect the horizontal velocity.
3.3 Projectile Motion
Example 3 A Falling Care Package
The airplane is moving horizontally with a constant velocity of +115 m/s at an altitude of 1050m. Determine the time requiredfor the care package to hit the ground.
y ay vy voy t-1050 m -9.80 m/s2 0 m/s ?
3 . 3 P r o j e c t i l e M o t i o n
?0 m / s- 9 . 8 0 m / s 2- 1 0 5 0 m
tv o yv ya yy
221 tatvy yoy 2
21 tay y
s 6.14
sm9.80
m 1050222
ya
yt
Example: The Velocity of the Care Package
What are the magnitude and direction of the final velocity ofthe care package?
3.3 Projectile Motion
14.6 s0 m/s?-9.80 m/s2-1050 m
tvoyvyayy
y ay vy voy t-1050 m -9.80 m/s2 ? 0 m/s 14.6 s
sm143
s 6.14sm80.90 2
tavv yoyy
3.3 Projectile Motion
Conceptual Example 5 I Shot a Bullet into the Air...
Suppose you are driving a convertible with the top down.The car is moving to the right at constant velocity. You pointa rifle straight up into the air and fire it. In the absence of airresistance, where would the bullet land – behind you, aheadof you, or in the barrel of the rifle?
3.3 Projectile Motion
Example 6 The Height of a Kickoff
A placekicker kicks a football at and angle of 40.0 degrees andthe initial speed of the ball is 22 m/s. Ignoring air resistance, determine the maximum height that the ball attains.
3 . 3 P r o j e c t i l e M o t i o n
ov
oxv
oyv
sm1440sinsm22sin ooy vv
sm1740cossm22sin oox vv
3.3 Projectile Motion
14 m/s0-9.80 m/s2?
tvoyvyayy
3 . 3 P r o j e c t i l e M o t i o n
1 4 m / s0- 9 . 8 0 m / s 2?
tv o yv ya yy
yavv yoyy 222 y
oyy
a
vvy
2
22
m 10
sm8.92
sm1402
2
y
3.3 Projectile Motion
Example 7 The Time of Flight of a Kickoff
What is the time of flight between kickoff and landing?
3.3 Projectile Motion
?14 m/s-9.80 m/s20
tvoyvyayy
3 . 3 P r o j e c t i l e M o t i o n
?1 4 m / s- 9 . 8 0 m / s 20
tv o yv ya yy
221 tatvy yoy
2221 sm80.9sm140 tt
t2sm80.9sm1420
s 9.2t
3 . 3 P r o j e c t i l e M o t i o n
E x a m p l e 8 T h e R a n g e o f a K i c k o f f
C a l c u l a t e t h e r a n g e R o f t h e p r o j e c t i l e .
m 49s 9.2sm17
221
tvtatvx oxxox
3.3 Projectile Motion
Conceptual Example 10 Two Ways to Throw a Stone
From the top of a cliff, a person throws two stones. The stoneshave identical initial speeds, but stone 1 is thrown downwardat some angle above the horizontal and stone 2 is thrown atthe same angle below the horizontal. Neglecting air resistance,which stone, if either, strikes the water with greater velocity?
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