9 motion in a plane

MOTION IN A PLANE

PROJECTILE MOTION

Motion in a Plane

refers to the motion of an

object traversing a curved

path which lies in a fixed

plane

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

ex. bullet shot from a gun

bomb released from an

aircraft

a ball thrown horizontally

Projectile motion is a combination

of:

1. constant horizontal velocity

vxo = vx = constant

ax = constant = 0

2. uniformly accelerated vertical

motion

ay = constant = g

Range, R

the horizontal distance from

the starting point to the point

at which the projectile return to

its original level

maximum horizontal

displacement

Time of Flight, T

the time that elapses from

the instant the projectile is

released until it hits the

ground

Equations for Projectile

Motion

are based on equations for

uniformly accelerated motion

a. An object which is given an

initial horizontal velocity, vxi

b. An object which is given an

initial velocity, vi at a

certain angle θ with the

horizontal

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.

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.

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?

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

c. the time required to return

to its original level

d. maximum height reached

e. the range

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.

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?

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?