Motion in a Plane
Plane - 2 dimensional surface
What kinds of objects have
Objects
Moving
Planets around sun
Pendulums
Projectiles
Human Cannonball
Projectile Fired Horizontally
Review Object projected horizontally
1. Viy = ?
2. ay = ?
3. Horizontal Velocity? (no air friction)
Vix = Vx = Constant
Horizontal Distance Traveled
4 objects thrown horizontally, same height, at various speeds.
Compare their:
Object is thrown horizontally,
Ex) A baseball is thrown horizontally from a grandstand 20 m above ground at speed of 10 m/s.
Step 3 - Substitute and Solve
dy = Viyt + ˝ayt2
20
m = 0 + ˝(9.8 m/s2)t2
t = 2 seconds
(b) What is the projectile's maximum range before it hits ground?
(b) What is the projectile's maximum range before it hits ground?
Range?
Range (dx)
Range
Horizontal Displacement (dx)
dx =Vxt
= (10m/s)2 secs
= 20 m
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Review Which velocity is constant for all spheres?.
Vx
AP Question Hewitt Question A cannonball is fired horizontally at 10 m/s from a cliff. Its speed one second
after being fired is about A. 10 m/s.
Vx = Vy = 10 m/s V = 14 m/s
AP Physics Review of freefall
Ex) Compare the time it takes for a whiffle ball to go up with the time it takes to reach its initial position.
Takes longer to return from peak. Friction would cause avg. vel. to be less on the way down.
Ex) A baseball is dropped from the top of a bleachers from a height of 80.‑meters. At the same time, another ball is thrown from horizontally. Both balls hit level ground, 50. m apart. (Air resistance is negligible.)
Find the horizontal velocity of the ball thrown.
Vx = dx/t
Time in air ∆dy = Viyt + 1/2ayt2
∆dy = 1/2ayt2
80 m = (4.9 m/s2)t2
t = 4 sec
Vx = dx/t
Vx = dx/t = 50 m/4 sec
= 13 m/s
Ex) An object moving horizontally with speed V falls off the edge of a vertical cliff and lands a distance d from the base of the cliff.
How far from the base of the cliff would the object land if the height of the cliff was doubled?
dx = Vxt = d dy = 1/2at2
double dy then t increased by radical 2
(radical 2)d or 1.4d
Ex) From a cliff of height 28.8 m above the ground, a ball is thrown horizontally with an initial velocity of 7.0 m/s.
What is the range of the ball?
dx = Vxt
∆dy = 1/2ayt2
28.8 m = 4.9t2
t = 2.4 sec
dx = Vxt = 7.0 m/s(2.4 s)
dx = 17 m
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