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mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Uniform Motion

Two cars are approaching an intersection. One is 2 miles south of the intersection and is moving at a constant speed of 30 mph. At the same time, the other car is miles east of the intersection and is moving at a constant speed of 40 mph. Build a model that expresses the distance d between the cars as a function of the time t.

Let me see

I am thinking Pythagoras in terms of his famous theorem a^2 + b^2 = c^2.

I am also thinking distance formula: D = rt.

Car 1 is 2 miles south of the intersection traveling at 30 mph.

This leads me to (30t + 2).

Car 2 is 3 miles east of the intersection traveling at 40 mph.

This leads me to (40t + 3).

We want D(t).

My model is D(t) = a^2 + b^2, which becomes D(t) = (30t + 2)^2 + (40t + 3)^2.

You say?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,637

Re: Uniform Motion

Nearly there. The cars are approaching the intersection so you need to subtract the rt distances from 2 and 3 so they get closer.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: Uniform Motion

Nearly there. The cars are approaching the intersection so you need to subtract the rt distances from 2 and 3 so they get closer.

Bob

Can you set it up for me?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,637

Re: Uniform Motion

But you're almost there on your own.  As the cars are appraoching the junction the distance is getting less.

Car 1 is 2 miles south of the intersection traveling at 30 mph.

This leads me to (30t + 2).

Car 2 is 3 miles east of the intersection traveling at 40 mph.

This leads me to (40t + 3).

So, for exampe, make it 3 - 40t (t measured in hours)

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: Uniform Motion

But you're almost there on your own.  As the cars are appraoching the junction the distance is getting less.

Car 1 is 2 miles south of the intersection traveling at 30 mph.

This leads me to (30t + 2).

Car 2 is 3 miles east of the intersection traveling at 40 mph.

This leads me to (40t + 3).

So, for exampe, make it 3 - 40t (t measured in hours)

Bob

Perfect. I can take it from here. Please read my about my new self-study plan.