Motion in a Plane, Projectile Motion, Sample Problems

1. MOTION IN A
PLANE
PROJECTILE MOTION

2. Motion in a Plane
refers to the motion of an
object traversing a curved
path which lies in a fixed
plane

3. Projectile Motion
a motion in which an
object is given an initial
velocity and which is then
allowed to move under the
action of its weight (or
gravity) alone

4. ex. bullet shot from a gun
bomb released from an
aircraft
a ball thrown horizontally

5. Projectile motion is a combination
of:
1. constant horizontal velocity
vxo = vx = constant
ax = constant = 0
2. uniformly accelerated vertical
motion
ay = constant = g

7. Range, R
the horizontal distance from
the starting point to the point
at which the projectile return to
its original level
maximum horizontal
displacement

8. Time of Flight, T
the time that elapses from
the instant the projectile is
released until it hits the
ground

9. Equations for Projectile
Motion
are based on equations for
uniformly accelerated motion

10. a. An object which is given an
initial horizontal velocity, vxi

11. b. An object which is given an
initial velocity, vi at a
certain angle θ with the
horizontal

12. Exercises
1. A stone is thrown with a
velocity of 35 m/s in a
horizontal direction from the
top of a tall building. Find its
velocity and displacement
after 2 seconds.

13. 2. A ball is thrown horizontally
with a velocity of 40 m/s
from a window 44.1 m from
the ground. Find the time of
flight and the range.

14. 3. A stone is thrown horizontally
from a building 122.5m high. If
the stone travels 25 m before
striking the ground, after how
many seconds will it reach the
ground? What is its initial
velocity?

15. 4. A ball is thrown at 38.7o
above the horizontal with a
speed of 32 m/s. Find:
a. the horizontal and vertical
components of the initial
velocity.
b. the magnitude of velocity
after 3 seconds

16. c. the time required to return
to its original level
d. maximum height reached
e. the range

17. SW ½ cross.
1. A bullet has a speed of
2000 ft/s as it leaves a rifle.
If it is fired horizontally from
a cliff 24 ft above a lake, find
the range and time of flight
of the bullet.

18. 2. Jude threw a ball horizontally
at a speed of 12 m/s, from a
third floor building, 20 m high.
Ignoring air resistance, how
long will it take for the ball to
reach the ground? How far from
the building will it strike?

19. 3. A projectile is fired at an angle
of 30o with the horizontal with a
speed of 600 m/s. Find the
horizontal and vertical
components of the initial
velocity. What is the maximum
height, range, and time of
flight?