EXAMPLE PROBLEMS
Projectile Motion
A BALL IS THROWN HORIZONTALLY FROM THE
TOP OF A BUILDING 47.7 M HIGH. THE BALL
STRIKES THE GROUND AT A POINT 108 M FROM
THE BASE OF THE BUILDING.
A. Find the time the ball is in motion.
B. Find the initial velocity
C. Find the x component of the velocity just before it
hits the ground
D. Find the y component of the velocity just before it
hits the ground
THE TIME THE BALL IS IN THE AIR
Is gravity effecting it?
Yes, use the vertical equations.
D=1/2gt2
√2d/g
2*47.7/9.8
√9.7=3.12s
INITIAL VELOCITY OF THE BALL
V=d/t
108/3.12
V=34.6
FIND THE X COMPONENT OF THE VELOCITY
JUST BEFORE IT HITS THE GROUND
The same as the initial velocity
FIND THE Y COMPONENT OF THE VELOCITY
JUST BEFORE IT HITS THE GROUND
V=gt
V=-9.8*3.12
V=-30.5765
m/s
***Remember
it is falling down
and gravity would be negative
AN ARROW IS SHOT AT A 33⁰ ANGLE WITH THE
HORIZONTAL. IT HAS A VELOCITY OF 54 M/S
A. How high will it go?
B. What horizontal distance will it travel?
54m/s
33⁰
vy
Vx
Sin 33 =y/54
Sin 33 *54
=29.41 m/s
Vertical speed
Cos 33=x/54
Cos 33 * 54= 45.28m/s
Horizontal speed
Look at your vertical equations
D=1/2gt2
V=gt
Let’s combine these two equations using substitution
method.
t=v/g
d=1/2 g(v/g)2
d=44.13 m
NOW LETS SOLVE FOR THE HORIZONTAL
DISTANCE.
We solved for the horizontal velocity and now we
need to find an equation for the horizontal
distance.
D=vt and because of the trajectory we need to use
twice the time from the previous problem.
A DESCENT VEHICLE LANDING ON THE
MOON HAS A VERTICAL VELOCITY VECTOR
TOWARD THE SURFACE OF THE MOON OF
31.6 M/S. AT THE SAME TIME, IT HAS A
HORIZONTAL VELOCITY OF
At
53.2 M/S.
what speed does the
vehicle move along its
descent path?
At what angle with the
vertical is its path?
AT WHAT SPEED DOES THE VEHICLE
MOVE ALONG ITS DESCENT PATH?
31.6 m/s
R
•53.6 m/s
a2+b2=c2
AT WHAT ANGLE WITH THE
VERTICAL IS ITS PATH?
31.6 m/s
R
θ=?
•53.6 m/s
tan θ=o/a
Θ=tan-1 (o/a)
JANET JUMPS OFF A HIGH
DIVING PLATFORM WITH A
HORIZONTAL VELOCITY OF 2.83
M/S AND LANDS IN THE WATER
2.2S LATER.
A.
How high is the platform?
B. How far from the base of
the platform does she land?
A IS ASKING FOR THE VERTICAL DISTANCE
2
D=1/2gt
B IS ASKING FOR HORIZONTAL DISTANCE
D=vt
0
