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# Thread: Precalculus Questions (Projectile Motion)

1. ## Precalculus Questions (Projectile Motion)

Well I have a precalculus final today and I need to know a few things if any of you can help me out.

1) Solving projectile motion problems for an object falling off a cliff. (Time it akes to land, distance traveled, velocity, etc)

2) Solving projectile motion problems for an object launched at an angle (ex. kicking a ball, hitting a golfball, etc; time it takes, max height reached, distance traveled, etc)

All help is appreciated. Thanks.

-Gix

2. Originally Posted by Gix
1) Solving projectile motion problems for an object falling off a cliff. (Time it akes to land, distance traveled, velocity, etc)
These are mostly a matter of knowing wich equation to use, are you given such equations, or are you expected to use basic integration/differentiation here?

Originally Posted by Gix
2) Solving projectile motion problems for an object launched at an angle (ex. kicking a ball, hitting a golfball, etc; time it takes, max height reached, distance traveled, etc)
For these, remember that horizontal and vertical motion can be calculated independently. Suppose you have an initial velocity v0 and an angle θ (measured with respect to horizontal) at wich the object is launched:
v0x = v0 sin θ
v0y = v0 cos θ

3. Originally Posted by Oscuro
These are mostly a matter of knowing wich equation to use, are you given such equations, or are you expected to use basic integration/differentiation here?
I wasn't given any equations. My teacher went over it briefly in class and then was like "It's on the final!"

I never paid attention in Physics either.

Thanks for the other equations.

-Gix

4. You only need to remember the equation for position given acceleration, time and initial velocity. Everything else can be figured out by splitting up the horizontal and vertical vectors and by using simple trig.

For example, for number one, you'll know acceleration (the acceleration due to gravity) and you'll have to be given everything except what you're asked to solve for. So if you're asked to solve for how long it takes to get to the ground, you'll be given the initial position and the initial velocity. If you're asked to find out how high the cliff is you'll be given the time it takes to fall and the initial velocity, which may be zero.

For a projectile launched at an angle, you'll probably just be given the downward acceleration (the acceleration due to gravity) and you'll assume zero air resistance. Breaking the velocity into its x and y components is simple trig. The x position will be easy because you'll have a constant velocity. All you have to do is treat the y position as if the object were lanuched striaght upwards. You'll know the initial position, the initial velocity and the acceleration, probably just due to gravity. You just have to find out how long it takes to get so the vertical velocity is zero and then it turnes into the cliff problem.

5. Some more equations:

v = at + v0

... to find current velocity of the object at time t given acceleration and initial velocity (which is 0 if an item is dropped, will have some value if an item is launched)

x = (1/2)at^2 + v0t + x0 (this is the indefinite integral of the above equation)

... to find the position of the object at time t given acceleration, initial velocity, and initial position.

An example:
Let's say you drop a ball from a 100m cliff, ignoring wind resistance:

1) Find the velocity of the ball after 1.8 seconds
v = -9.8(1.8) + 0
v = -17.64 m/s

2) Find the position of the ball at t=3 seconds
x = (1/2)(-9.8)(3^2) + 0(3) + 100
x = 55.9m

3) Find the time t at which the ball strikes the ground
0 = (1/2)(-9.8)(t^2) + 0(t) + 100
-100 = (1/2)(-9.8)(t^2)
sqrt (-200/-9.8) = t
t ~= 4.518s

6. Originally Posted by Oscuro
Some more equations:

v = at + v0

... to find current velocity of the object at time t given acceleration and initial velocity (which is 0 if an item is dropped, will have some value if an item is launched)

x = (1/2)at^2 + v0t + x0

... to find the position of the object at time t given acceleration, initial velocity, and initial position.

An example:
Let's say you drop a ball from a 100m cliff, ignoring wind resistance:

1) Find the velocity of the ball after 1.8 seconds
v = -9.8(1.8) + 0
v = -17.64 m/s

2) Find the position of the ball at t=3 seconds
x = (1/2)(-9.8)(3^2) + 0(3) + 100
x = 55.9m

3) Find the time t at which the ball strikes the ground
0 = (1/2)(-9.8)(t^2) + 0(t) + 100
-100 = (1/2)(-9.8)(t^2)
sqrt (-200/-9.8) = t
t ~= 4.518s
I know from the title i wouldnt have a hope in hell of following this thread... I hate sucking at maths and physics, along with all other subjects.

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