FREE FALL
Problem Set # 6:
1. A ripe mango, hanging from a branch, suddenly falls to the
ground. If the mango acquired a final velocity of 8 m/s when it
hit the ground, how high was the mango before it fell?
2. A ball is thrown vertically upward with a velocity of 12 m/s.
a) At what height is the ball 1 s later?
b) 2 s later?
c) What is the maximum height the ball reaches?
VOLLEYBALL BASKETBALL
Science, Technology,
Engineering, and Mathematics
General
LESSON 8
Physics 1
❑ Motion in Two Dimensions:
Projectile Motion
Learning Objectives
1. Explain projectile motion.
2. Solve problems involving horizontally-
launched and non-horizontally launched
projectiles.
3. Calculate the range, time of flight, and
maximum heights of projectiles.
PROJECTILE MOTION
Projectile Motion– is the motion of an object
thrown or projected into the air, acted upon only by
acceleration due to gravity.
PROJECTILE MOTION
Projectile - any object that moves or that is
projected into the air, acted upon ONLY by acceleration
due to gravity.
PROJECTILE MOTION
Point of projection - the point from which the
object is projected in air.
PROJECTILE MOTION
Velocity of projection - The velocity with which an
object is projected in air.
PROJECTILE MOTION
Angle of projection - The angle with the horizontal
at which an object is projected in air.
PROJECTILE MOTION
Trajectory - The parabolic path followed by a
projectile in air.
PROJECTILE MOTION
Time of Flight (t) - time taken by the projectile to
cover the entire trajectory.
PROJECTILE MOTION
Maximum Height (H) - It is the maximum vertical
distance travelled by the projectile from the ground
level during its motion.
PROJECTILE MOTION
Horizontal Range (R) - it is the horizontal distance
travelled by the projectile during entire motion.
PROJECTILE MOTION
▪ Projectiles move in 2-dimensions.
▪ Projectile Motion combines Vertical Motion and
Horizontal Motion.
▪ The vertical and horizontal motion of a projectile are
independent of each other.
PROJECTILE MOTION
▪ The vertical motion of a projectile is not affected by its
horizontal motion
meaning: The vertical motion of a projectile is
identical to an object in free fall.
✓ The vertical velocity (𝑣𝑦 ) of a projectile changes by 9.8
m/s each second.
✓ The vertical acceleration (𝑎𝑦 ) caused by gravity is -9.8
m/s2.
PROJECTILE MOTION
▪ The horizontal motion of a projectile is not affected by its
vertical motion.
meaning: meaning the projectile will travel the same
horizontal distance as it would if it were simply rolling on a flat
surface in the absence of friction.
✓ The horizontal velocity (𝑣𝑥 ) of a projectile is constant (a never
changing in value).
✓Gravity DOES NOT work horizontally to increase or decrease
the velocity.
✓ Therefore, there is no horizontal acceleration (𝑎𝑥 =0 m/s2) .
HORIZONTALLY-LAUNCHED
PROJECTILE MOTION
Projectiles which have NO upward trajectory and NO
initial VERTICAL velocity.
Four (4) Kinematic Equations
HORIZONTAL MOTION VERTICAL MOTION
1. 𝑣𝑓𝑥 = 𝑣𝑖𝑥 + 𝑎𝑥 𝑡 1. 𝑣𝑓𝑦 = 𝑣𝑖𝑦 + 𝑔𝑡
𝑣𝑓𝑥 +𝑣𝑖𝑥 𝑣𝑓𝑦 +𝑣𝑖𝑦
2. 𝑑𝑥 = 𝑡 2. 𝑑𝑦 = 𝑡
2 2
3. 𝑣𝑓𝑥 =
2
𝑣𝑖𝑥 2
+ 2𝑎𝑥 𝑑𝑥 3. 𝑣𝑓𝑦 =
2
𝑣𝑖𝑦 2
+ 2𝑔𝑑𝑦
1 1
4. 𝑑𝑥 = 𝑣𝑖𝑥 𝑡 + 𝑎𝑥 𝑡 2
4. 𝑑𝑦 = 𝑣𝑖𝑦 𝑡 + 𝑔𝑡 2
2 2
HORIZONTALLY-LAUNCHED
PROJECTILE MOTION
Sample Problem 1:
A pool ball leaves a 0.60-meter high table with an
initial horizontal velocity of 2.4 m/s. Calculate the time
required for the pool ball to fall to the ground and the
horizontal distance between the table’s edge and the
ball’s landing location.
HORIZONTALLY-LAUNCHED
PROJECTILE MOTION
Sample Problem 2:
A soccer ball is kicked horizontally off a 22.0-meter
high hill and lands a distance of 35.0 meters from the
edge of the hill. Determine the initial horizontal
velocity of the soccer ball.
NONHORIZONTALLY-LAUNCHED
PROJECTILE MOTION
Projectiles which have projected at an angle.
NONHORIZONTALLY-LAUNCHED
PROJECTILE MOTION
Since the projectile was launched at an angle, the
initial velocity MUST be broken into components!!!
𝑣𝑖𝑥 = 𝑣𝑖 cos 𝜃
𝑣𝑖𝑦 = 𝑣𝑖 sin 𝜃
NONHORIZONTALLY-LAUNCHED
PROJECTILE MOTION
Sample Problem 2:
A long-jumper leaves the ground with an initial velocity
of 12 m/s at an angle of 28° above the horizontal.
Determine the time of flight, the horizontal distance,
and the peak of height of the long-jumper.
PROJECTILE MOTION
Problem Set # 7:
1. A medical doctor threw a small medical package horizontally
at 10 m/s from the 5th floor of the hospital 15 m high.
a) How long does the medical package take to reach the ground
floor?
b) How far from the base of the building does the medical
package strike the ground?
PROJECTILE MOTION
Problem Set # 7:
2. James Yap threw the ball with an initial velocity of 30 m/s 30ᴼ
above the horizontal.
a) How long it took the ball to land?
b) How high the ball flew?
c) What its range was?
