## Chapter 1 Kinematics

chibean
Posts: 11
Joined: Fri Jan 03, 2020 12:10 pm

### Chapter 1 Kinematics

Can you clarify how to solve for projectile motion and possibly give an example. Also how would you determine when to use sine or cosine to determine motion on an inclined plane? Also an example for this one to would be helpful. Thank you.
NS_Tutor_Mathias
Posts: 616
Joined: Sat Mar 30, 2019 8:39 pm

### Re: Chapter 1 Kinematics

To help me formulate a reply more quickly and a bit more pointedly, please in the future point at a particular example that you have attempted to work through, and where you encountered a problem you weren't able to solve.

Projectile motion:
Virtually all MCAT projectile motion ignores air resistance, so you are generally only answering the question of how long a projectile travels and how far it travels, where how long it travels is bounded by the time it takes to hit the ground (dependent only in the initial vertical velocity and the downward acceleration, often only gravity) and how far it travels is simply the horizontal velocity component multiplied by the travel time.

As for how to find horizontal and vertical components of the launch velocity, here:
vector_decomposition.png
That should pretty much walk you through it. Notice that this reasoning works for any vector decomposition, including, if need be, inclined planes.

Inclined planes:
All you need to do is decompose the gravity vector into two components, one parallel to the plane and one perpendicular to the plane. You do this using the same trigonometric logic. So as an exercise, I'll provide you with an image again:
decompositiondemo.png
Looking at this, can you tell me, given angle theta, how to determine the magnitude of the vector along the plane (this one will accelerate the box down the plane) and the magnitude of the vector into the plane (this one will only really generate the normal force - relevant if this were a friction problem. I will tell you that this situation is completely analogous to the vector decomposition demonstrate above.
chibean
Posts: 11
Joined: Fri Jan 03, 2020 12:10 pm

### Re: Chapter 1 Kinematics

Would you just add the 2 together? (gpeprendicular= g cos theta) + ( gparellel =g sin theta)

And would you just need to know the angle to solve it?
NS_Tutor_Mathias
Posts: 616
Joined: Sat Mar 30, 2019 8:39 pm

### Re: Chapter 1 Kinematics

chibean wrote:
Sun Jan 19, 2020 3:28 pm
gparellel =g sin theta
Just this alone. That would give you the component that accelerates the box down the incline. Done.

And you can sanity check this:
For a box sitting on flat ground, theta = 0. So g sin(0) = 0. This is saying that a box on flat ground stays where it is. Seems about right!

For a box falling straight down (maybe there is a decorative, friction-free wall it is touching on one side), theta = 90. So gsin(90)=g. This is saying that objects in free fall accelerate at g. That also checks out.