Name ___________________________
Hour_______ Date_________________
Physics
2D Kinematics: Problem Solving- No angles
Solving 2D kinematics problems are quite similar to solving 1D motion problems. You use the same equations
(they just look a little different) and you still make a list of known and unknown variables.
Here are the equations that you could potentially use to solve 2D kinematics problems.
Vertical Motion of a Projectile that falls from rest
vfy = viy + ayt
vfy2 =viy2 + 2aydy
dy = viyt + ½ ayt2
Horizontal motion of a projectile
vx = vix = constant (because no force acts in the x direction, therefore no acceleration)
dx = vxt
Notice that in these equations, time does not have a subscript. That is because time is not a vector quantity and
will be the same, regardless if the object is moving in the horizontal or vertical directions.
In this packet, I will show you, step-by-step, how to solve 2D kinematics problems. Then you will attempt to solve
some them on your own.
Example 1:
The Royal Gorge Bridge in Colorado rises 321 m above the Arkansas River. Supposed you kick a rock horizontally
off the bridge. The magnitude of the rock’s horizontal displacement is 45.0 m. Find the speed at which the rock
was kicked.
Step 1: Read the entire problem.
Step 2: Make a list of your knowns and unknowns. This list should include vi, vf, a, d, and t. But it will need to have
all of these quantities listed for both the x and y directions.
viy is 0 because the object is
ax is ALWAYS 0 because
x
y
falling. When an object falls, the
there is no force acting in
?
vi
0
initial velocity in the y direction
the x direction. Gravity only
is 0 m/s
acts in the y direction.
vf
Given in the problem. dx can
also be called “horizontal
displacement”
0 m/s2
45.0 m
a
-9.8 m/s2
d
-321 m
t
2
ay isis ALWAYS
ay
ALWAYS -9.8
-9.8 m/s
m/s2
because
because
this is the acceleration due to
gravity. It is always present in the
y direction.
Given in the problem. It is
negative because the rock falls
this distance downward.
Step 3: Determine what you need to find.
We know that ultimately we need to find vix. It asked this in the question.
Step 4: Chose an equation.
The only equation we have that has any sort of vx in it is dx = vxt.
Well, we know dx. And we need to find vx. But what about time?
We will need to solve for this also.
x
?
vi
y
0
vf
0 m/s2
45.0 m
?
a
-9.8 m/s2
d
-321 m
t
?
Remember that if we know time in one direction, we know it in both.
Do we have enough information to solve for time using y-direction information?
Yes.
Chose an equation (from the vertical motion equations):
We don’t want to use any equation that has vfy in it because we don’t know it and don’t have enough information
to solve for it.
This only leaves one equation:
dy = viyt + ½ ayt2
Step 5: rearrange the equation.
dy = viyt + ½ ayt2
dy = ½ ayt2
t = √2𝑑𝑦 /𝑎𝑦
Cancelled out because viy = 0
Step 6: Solve using grids
Step 7: Use this information and plug it into the original equation: dx = vxt. USE GRIDS TO SOLVE.
You just solved your first 2D kinematics equation! Give yourself a round of applause!
In this second example you will fill in the blanks as you go through the steps. The answers are on the very last
page of this packet
Example 2: Carla rolls a marble down a ramp and off a table with a horizontal velocity of 1.2 m/s. The marble
falls 0.51 m from the table’s edge. How high is the table?
Step 1: Read the entire problem.
Step 2: Make a list of your knowns and unknowns. This list should include vi, vf, a, d, and t. But it will need to have
all of these quantities listed for both the x and y directions.
x
y
vi
vf
a
d
t
Step 3: Determine what you need to find.
Ultimately we know we need to find ___________________.
Step 4: Chose an equation.
There are 2 equations with _____________________ in them.
Which is the better one to use? ___________________
Based on this equation we also need to find _______________________.
Remember that if we know _____________________ in one direction, we know it in both.
Do we have enough information to solve for ____________ using ______-direction information?
This only leaves one equation:
_____________________
Step 5: rearrange the equation.
___________________________
_______.
Step 6: Solve using grids
Step 7: Use this information and plug it into the original equation: ____________________. USE GRIDS TO SOLVE.
Now you try one, all on your own. Show work in space provided.
Example 3: Bert is standing on a ladder throwing apples into a basket sitting on the ground. Bert is 3.0 m above
the basket on the ladder, and the ladder is 2.0 m away from Bert. How fast must Bert throw the apples
(horizontally) in order for them to land in the basket? (answer: 2.56 m/s)
One more. Show work in space provided.
Example 4: A ball is thrown from a height of 2.35 m above the ground. The ball lands 5.0 m from where it was
thrown. At what speed was the ball thrown horizontally? (answer: 7.22 m/s)
You are ready to start working on “Projectile Workhseet #2”.