Finding Time and Distance in a Lion-Monkey Chase

[Juan42]

Homework Statement

A monkey first notices a lion attacking when the lion is 12.5 m away and moving toward the monkey at a speed of 5 m/s. The monkey begins to accelerate away from the lion at 3 m/(s^2) and the lion simultaneously begins to accelerate at 2 m/(s^2). (a) How long does the monkey's escape last? (b) How far has the monkey traveled when the lion catches up with it? Answers: (a) 5 seconds; (b) 37.5 m

Homework Equations

(1) V = at + Vo
(2) V^2 = Vo^2 + 2a(X - Xo)

The Attempt at a Solution

At first I tried finding the time using the lion's information. I used (2), but I only accounted for the distance that lion traveled until it got to monkey's inital position before the monkey noticed and tried to escape the lion. I just got the answers I started with. I can't seem to know where exactly to start to find the answer that the instructor gave me. I was wondering if I could get some help with this.

 

[gneill]

Homework Statement

A monkey first notices a lion attacking when the lion is 12.5 m away and moving toward the monkey at a speed of 5 m/s. The monkey begins to accelerate away from the lion at 3 m/(s^2) and the lion simultaneously begins to accelerate at 2 m/(s^2). (a) How long does the monkey's escape last? (b) How far has the monkey traveled when the lion catches up with it? Answers: (a) 5 seconds; (b) 37.5 m

Homework Equations

(1) V = at + Vo
(2) V^2 = Vo^2 + 2a(X - Xo)

The Attempt at a Solution

At first I tried finding the time using the lion's information. I used (2), but I only accounted for the distance that lion traveled until it got to monkey's inital position before the monkey noticed and tried to escape the lion. I just got the answers I started with. I can't seem to know where exactly to start to find the answer that the instructor gave me. I was wondering if I could get some help with this.

Hi Juan42, Welcome to Physics Forums.

You'll need to use both sets of information (lion and monkey) to solve the problem. The information for the lion will let you write an equation for its position with respect to time, and the information for the monkey will let you do the same for the monkey. Be sure to write the equations with respect to a common coordinate system (that is, pay attention to the initial position difference between the lion and monkey).

The two position equations should intersect (have the same position value) for at least one value of time.

 

[Juan42]

It took me a sec to think it over, but I understand what you mean by putting them on the same axis. Anyway, thanks.