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## AP®︎/College Physics 1

### Unit 2: Lesson 3

Graphs of projectile motion

# Projectile motion graphs review

Review the key concepts and skills for two-dimensional projectile motion, including analyzing projectile motion graphs.

## Key Terms

TermMeaning
ProjectileObject moving through the air, either initially thrown or dropped, subject only to the effects of gravity.
TrajectoryThe path of a projectile, which is parabolic in two dimensions.
Projectile MotionMovement of an object through the air, subject only to the effects of gravity.

## Common mistakes and misconceptions

1. Remember: What happens in the vertical direction does NOT affect the horizontal direction, and vice versa. An object’s horizontal position, velocity, or acceleration does not affect its vertical position, velocity, or acceleration. These motions can only be related by the time variable t.
2. It is easy to forget that horizontal motion has constant velocity (and zero acceleration!) while vertical motion has constant acceleration. This means for projectile motion, the starting velocity in the x-direction will be the same as the final velocity in the x-direction, while the starting and ending velocities in the y-direction will be different because of acceleration due to gravity.

For deeper explanations, see our video on projectile motion graphs.
To check your understanding and work toward mastering these concepts, check out the exercises on identifying graphs for projectiles and comparing multiple trajectories.

## Want to join the conversation?

• why does the horizontal motion not affect the vertical motion? If the object is dropping faster doesn't the horizontal motion decrease because it isn't traveling any further, rather downwards.
• For this case, no, because they are assuming there is no air resistance.
• Does vertical motion really have a constant acceleration? plz correct me if i am wrong, but since Acceleration is a vector quantity because it has both magnitude and direction. i.e. When an object has a negative acceleration (it's slowing down), the acceleration occurs in the opposite direction as the movement of the object--> this is the case from start till max height then acceleration will be in the same direction as the movement of the object and becomes positive. so i think we better say vertical motion has a constant "absolute" acceleration or "vertical motion has an acceleration of constant magnitude. plz correct me if i am wrong
• On Earth, we use the constant g = -9.8 m/s^2 to represent the constant acceleration due to gravity that pulls us to Earth's center of mass. Whether you use +g or -g depends on how you define your system; some people like to use +g and switch all their variables around. However, g always represents motion towards the center of Earth. The direction of g depends on how you define the system.
• Why does the horizontal motion move at a constant velocity? Is this common sense?
• The velocity of an object remains constant until it is acted on by an accelerating force. Gravity is a vertical force. So if you say that air resistance is negligible, the horizontal velocity will not change.. At least not until it impacts the ground.
• What is "projectile motion"? Are there other types of motion?
• Projectile motion is the movement of an object through the air while only considering gravity. Other types of motion get more complicated and can consider, for example, both gravity and air resistance. Hope this helps!
• how does the trajectory and velocity vectors actually effect the projectile?
• Trajectory and velocity vectors actually don't affect the projectile, they describe its comportament
• in the last quiz, there was 1 confusing question about calculating time in the air(Tower of Pisa),
let's say that we have 2 projectile(p1,p2) 20m from the ground, then we dropped p1(change in x-axis=0m)then threw p2(change in x-axis=18m)
why they took the same amount of time in the air? why we only calculating the y-axis speed?
sorry for the bad grammar but I hope you understand the question
• This is an example of Horizontally launched projectile (initial velocity in y-direction = uy = 0)
time taken for total displacement in x and y directions are the same (the same object remember)!
of course you can use ux(initial velocity in the x-direction) but it takes a bit more time to solve for time (excuse the bad pun :P),
rather, consider this:
Δy = uyt +1/2 at^2
uy = 0
Δy = 1/2at^2
t = rt(Δy*2/a)
as 2/a will be constant for all,
we can say t depends on Δy,
or t ∝ Δy

you can try for Δx = uxt + 1/2at^2
here a = 0
Δx = uxt
t = Δx/ux
this is cool and everything but you have to actually solve Δx/ux :(
(remember ux don't necessarily have to be constant)
that is why we use Δy, much quicker
(1 vote)
• I do not understand why does the blue scenario have vertical velocity? he is moving in horizontal direction only!
(1 vote)
• Joseph Chai
4 years ago
Posted 4 years ago. Direct link to Joseph Chai's post “why does the horizontal m...”
why does the horizontal motion not affect the vertical motion? If the object is dropping faster doesn't the horizontal motion decrease because it isn't traveling any further, rather downwards.
(1 vote)
• Why an object that is dropped horizontally doesn't change its position over time?
(1 vote)
• When something is thrown at an angle(for eg. golf ball), if the ques asks about vertical velocity component in a graph, does it have to be upright vertical velocity component? and if they ask vertical velocity and trajectory then would the ans still be vertical or at an angle (the path followed by a ball), this was a ques in one of the quizzes(comparing multiple trajectories Que 3 I guess)
(1 vote)