Name
Date
Pd
Particle Models in Two Dimensions Worksheet 3:
Projectile Motion Problems
FOR ALL PROBLEMS USE SUBSCRIPTS TO DISTINGUISH X & Y DIRECTIONS
1. The movie "The Gods Must Be Crazy" begins with a pilot dropping a bottle out of an
airplane. A surprised person below, who thinks it is a message from the gods, recovers it. If
the plane from which the bottle was dropped was flying at a height of 500m, and the bottle
lands 400m horizontally from the initial dropping point, how fast was the plane flying when
the bottle was released?
LABELED SKETCH with MOTION DIAGRAM
KNOWN QUANTITIES
y  500m
x  400m
a x  0m / s / s
a y  10m / s / s
UNKNOWNS
t
vix
viy  0m / s
POSSIBLE EQUATIONS
1
y  a y t 2  viy t
2
1
m
m
500m  (10 2 )(t 2 )  0 t
2
s
s
2
100  t
10  t
x  vix t
400m  vix (10 s )
40
m
 vix
s
2. Suppose that an airplane flying 60 m/s, at a height of 300m, dropped a sack of flour. How far
from the point of release would the sack have traveled when it struck the ground? Where
will the plane be in relation to the sack when the sack hits the ground? Illustrate your answer
carefully using the grid provided.
©Modeling Instruction 2013
1
U6 2D Motion - ws 3 v3.1
KNOWN QUANTITIES
m
vix  60
s
y  300m
a x  0m / s / s
a y  10m / s / s
viy  om / s
UNKNOWNS
t and ∆x
POSSIBLE EQUATIONS
1
y  a y t 2  viy t
2
1
m
m
300m  (10 2 )(t 2 )  0 t
2
s
s
2
60  t
7.7 s  t
x  vix t
x  60m / s(7.7 s)
x  464m
3. Tad drops a cherry pit out the car window 1.0 m above the ground while traveling down the
road at 18 m/s. How far, horizontally, from the initial dropping point will the pit hit the
ground? If the car continues to travel at the same speed, where will the car be in relation to the
pit when it lands?
LABELED SKETCH with MOTION DIAGRAM
Pit should land right below his hand because the pit has the same constant velocity in the x-dir as
the car.
©Modeling Instruction 2013
2
U6 2D Motion - ws 3 v3.1
KNOWN QUANTITIES
UNKNOWNS
m
s
y  1m
a x  0m / s / s
t and ∆x
vix  18
a y  10m / s / s
viy  om / s
POSSIBLE EQUATIONS
1
y  a y t 2  viy t
2
1
m
m
1m  (10 2 )(t 2 )  0 t
2
s
s
2
0.2  t
x  vix t
x  18m / s (0.45s )
x  8.1m
0.45s  t
4.
A student finds that it takes 0.20s for a
ball to pass through a set of timers a distance of 0.3
m apart on a level ramp. The end of the ramp is 0.92 m
above the floor.
a. What is the speed of the ball when it is passing through the timers?
KNOWN QUANTITIES
UNKNOWNS
POSSIBLE EQUATIONS
b. Where should a coin be placed so that the ball strikes it directly on impact with the ground?
KNOWN QUANTITIES
UNKNOWNS
POSSIBLE EQUATIONS
5.
Suppose now that the same ball, released from the same ramp (0.92 m high) struck a coin
placed 0.25 m from the end of the ramp.
a)
What was the ball's horizontal velocity?
KNOWN QUANTITIES
UNKNOWNS
POSSIBLE EQUATIONS
b)
How long did it take for the ball to pass through the same set distance of 0.3 m?
©Modeling Instruction 2013
3
U6 2D Motion - ws 3 v3.1
KNOWN QUANTITIES
©Modeling Instruction 2013
UNKNOWNS
4
POSSIBLE EQUATIONS
U6 2D Motion - ws 3 v3.1