Projectile Motion for an Object
Launched Horizontally
Ck12 Science
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Printed: September 22, 2015
AUTHOR
Ck12 Science
www.ck12.org
C HAPTER
Chapter 1. Projectile Motion for an Object Launched Horizontally
1
Projectile Motion for an
Object Launched Horizontally
• State the relationship between the vertical and horizontal velocities of a projectile launched horizontally.
• Find the time for a horizontally launched projectile to strike the ground.
• Calculate the range of a horizontally launched projectile.
The activity of bike jumping, like other sports that involve vector motions in perpendicular directions, requires more
physical practice than mathematical analysis. The laws of physics apply to the activity, however, whether the biker
is aware of them or not.
Projectile Motion for an Object Launched Horizontally
Objects that are launched into the air are called projectiles. The path followed by a projectile in motion is called
a trajectory. The image of the snowboarder in the chapter introduction showed his trajectory; every object has a
trajectory even when we cannot see it. Projectile motion, or the object’s trajectory, is described in terms of position,
velocity, and acceleration. Even with only an object’s current location, velocity, and acceleration, we can calculate
when and where the object will land. Our knowledge that perpendicular components of vectors do not affect each
other allow us to easily analyze the motion of projectiles.
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In the diagram, two balls (one red and one blue) are dropped at the same time. The red ball is released with no
horizontal motion and the blue ball is dropped but also given a horizontal velocity of 10 m/s. As the balls fall to the
floor, a photograph is taken every second so that in 5 seconds, we have 5 images of the two balls. Each vertical line
on the diagram represents 5 m. Since the blue ball has a horizontal velocity of 10 m/s, you will see that for every
second, the blue ball has moved horizontally 10 m. That is, in each second, the blue ball has increased its horizontal
distance by 10 m. This horizontal motion is due to the ball’s constant velocity.
The red ball was dropped straight down with no horizontal velocity and therefore, in each succeeding second, the
red ball falls straight down with no horizontal motion. The increasing distances between seconds in the red ball’s
motion indicates that this motion is accelerating.
A very important point here is that the vertical motion of these two balls is identical. That is, they each fall exactly
the same distance vertically in each succeeding second. The constant horizontal velocity of the blue ball has no
effect on its accelerated vertical motion. Therefore, the vertical motion of the blue ball can be analyzed exactly the
same as the vertical motion of the red ball.
Example Problem: If an arrow is fired from a bow with a perfectly horizontal velocity of 60.0 m/s and the arrow
was 2.00 m above the ground when the it was released, how far will the arrow fly horizontally before it strikes the
ground?
Solution: This problem is solved by determining how long it takes the arrow to fall to the ground in exactly the same
manner as if the arrow was dropped with no horizontal velocity. The time required for the arrow to fall to the ground
will be the same time that the arrow flies horizontally at 60.0 m/s, so
s
r
2d
(2)(2.00 m)
d = 12 at 2 solved for t =
=
= 0.639 s
a
9.80 m/s2
The time required for the fall is multiplied by the horizontal velocity to get the horizontal distance.
dhorizontal = (vhorizontal )(time) = (60.0 m/s)(0.639 s) = 38.3 m
Example Problem: A rock was thrown horizontally from a 100.0 m high cliff. It strikes the ground 90.0 m from the
base of the cliff. At what speed was it thrown?
Solution: We can calculate how long it takes for a rock to free fall 100.0 m and then divide this time into the
horizontal distance to get the horizontal velocity.
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Chapter 1. Projectile Motion for an Object Launched Horizontally
s
2d
(2)(100.0 m)
t=
=
= 4.52 s
a
9.80 m/s2
d 90.0 m
v= =
= 19.9 m/s
t
4.52 s
r
Summary
• Perpendicular components of vectors do not influence each other.
• The horizontal motion of a projectile does not influence its free fall.
Practice
Questions
The following video is a clip from Mythbusters, testing the "myth" that a bullet dropped at the same moment and
from the same height as one shot from a gun will also hit the ground instantaneously.
https://www.youtube.com/watch?v=abUBrQmI33Q
MEDIA
Click image to the left or use the URL below.
URL: http://www.ck12.org/flx/render/embeddedobject/112417
1.
2.
3.
4.
What was the problem the mythbusters had with the dropped bullet? Why was fixing this so important?
Why did they move the bullet being dropped to 360 ft away?
What was the final result?
What are some possible reasons that the bullets didn’t hit the ground at exactly the same time?
Review
Questions
1. If a bullet is fired from a high powered rifle at the exact time a duplicate bullet is dropped by hand near the
barrel of the rifle, which bullet will hit the ground first?
1. the one dropped straight down
2. the one fired horizontally
3. both will hit the ground at the same time
2. A cannon is fired from the edge of a small cliff. The height of the cliff is 80.0 m. The cannon ball is fired
with a perfectly horizontal velocity of 80.0 m/s. How far will the cannon ball fly horizontally before it strikes
the ground?
3. A cliff diver running 3.60 m/s dives out horizontally from the edge of a vertical cliff and reaches the water
below 2.00 s later. How high is the cliff and how far from the base of the cliff did the diver hit the water?
• projectile motion: A form of motion where a particle (called a projectile) is thrown obliquely near the earth’s
surface, it moves along a curved path under the action of gravity. The path followed by a projectile motion
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is called its trajectory. Projectile motion only occurs when there is one force applied at the beginning of the
trajectory after which there is no interference apart from gravity.
• trajectory: The path followed by an object in projectile motion.
References
1. Courtesy of PDPhoto.org. http://www.pdphoto.org/PictureDetail.php?mat=&pg=7672 .
2. Samantha Bacic. CK-12 Foundation .
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