Motion in a Plane
Objects
Moving
Review Object projected horizontally
1. V_{iy} = ?
2. a_{y} = ?
3. Horizontal Velocity? (no air friction)
V_{ix} = V_{x} = 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.
d_{y} = V_{iy}t + ˝a_{y}t^{2}
20
m = 0 + ˝(9.8 m/s^{2})t^{2}
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 (d_{x})
d_{x} =V_{x}t
= (10m/s)2 secs
= 20 m
Review
V_{x}
_{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.
V_{x} = d_{x}/t
Time in air ∆d_{y} = V_{iy}t + 1/2a_{y}t^{2}
∆d_{y} = 1/2a_{y}t^{2}
80 m = (4.9 m/s^{2})t^{2}
t =^{ }4 sec
V_{x} = d_{x}/t
V_{x} = d_{x}/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?
d_{x} = V_{x}t = d d_{y} = 1/2at^{2}
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?
d_{x} = V_{x}t
∆d_{y} = 1/2a_{y}t^{2}
28.8 m = 4.9t^{2}
t = 2.4 sec
d_{x} = V_{x}t = 7.0 m/s(2.4 s)
d_{x} = 17 m

