Predicting Collisions of 2 objects

[shockawave]

Predicting Collisions of 2 objects (EDITED)

Homework Statement

Object 1 is at the origin. Object 2 is currently at 10 meters east and 20 meters north(10, 20) moving directly north at 30m/s . If Object 1 is moving at 70m/s, at what angle would Object 1 have to travel in order to collide with Object 2. Approximately where would they intersect?

Homework Equations

I believe it you could use a system of equations.
mx+b = mx + b

To be honest with you it has been a while since i have taken physics and i don't really think we covered this type of scenario. This isn't my homework but it is vital that i know how to do this kind of problem because it relates to a video game that i am making.

The Attempt at a Solution

I have no clue where to begin in finding the direction.

I thought you would be able to solve a system of equations to find the coordinates so that

y_collision = m₁x₁+y₁-m₂x₂

I would also use the same method to find the x coordinate. However, i don't know how to calculate m₁ since the slope would also require a direction, which i do not know how to find..

 

[gneill]

Homework Statement

Object 1 is at the origin. Object 2 is currently at 10 meters east and 20 meters north(10, 20) moving directly north at 30m/s . If Object 1 is moving at 70m/s, at what angle would Object 1 have to travel in order to collide with Object 2. Approximately where would they intersect?

Homework Equations

I believe it you could use a system of equations.
mx+b = mx + b

To be honest with you it has been a while since i have taken physics and i don't really think we covered this type of scenario. This isn't my homework but it is vital that i know how to do this kind of problem because it relates to a video game that i am making.

The Attempt at a Solution

I have no clue where to begin in finding the direction.

I thought you would be able to solve a system of equations to find the coordinates so that

y_collision = m₁x₁+y₁-m₂x₂

I would also use the same method to find the x coordinate. However, i don't know how to calculate m₁ since the slope would also require a direction, which i do not know how to find..

Object 2 travels a known straight line and so you should be able to write parametric equations for its x and y coordinates with respect to time (that is, two equations: x2(t) and y2(t)).

For object 1 since you know the speed and not the angle, it could (theoretically) be located at any point on the circumference of a circle whose radius is a function of time as determined by its fixed speed. If you confine yourself to the upper half-circle, you should be able to write an expression that relates the possible values of x1 and y1 to the radius (think Pythagoras).

Can you write the equations?