need help with science

Question

a police officer is chasing a purse snacher down a street the thief starts 9 meters ahead of officer and can run 20meters in 4 seconds the police offocer can run 32 meters in 4 seconds how long does it take the officer to catch him

 

Answer 1

First, find the velocity of each (v = distance / time): 20m/4s = 5m/s for the thief and 32m/4s = 8m/s for the officer. Now, displacement (or distance from the origin) is: s = s₀ + vt (initial displacement plus velocity x time)

Thief starts 9m ahead so: s = 9 + 5t

Officer starts from 0m so: s = 8t

The officer catches the thief when their displacements are equal, so:

8t = 9 + 5t 

which you can now solve for t, by grouping like terms.

Answer 2

The way that I would solve this problem is by graphing both the purse snatcher (thief) and the police officer, and the point where they intersect is where the officer catches up to the thief. The y-axis can represent how many meters were run, and the x-axis can represent how many seconds it has taken. 

Step 1. Figure out the slope for both the thief and the officer.

Thief: Can run 20 meters in 4 seconds. If we write that as a slope, it would be 20 meters/4 seconds. We can simplify that down to 5 meters/second. Therefore our slope will be 5/1 or 5. 
Officer: Can run 32 meters in 4 seconds. If we write that as a slope, it would be 32 meters/4 seconds. We can simplify that down to 8 meters/second. Therefore our slope will be 8/1 or 8.

Step 2. Figure out the y-intercepts for both the thief and the officer. 

Thief: Started 9 meters ahead of the officer. So the y-intercept would be (0,9). 
Officer: Started 9 meters behind the theif. So the y-intercept would be (0,0). 

Step 3. Write the equations for the line for the thief and the officer.

Thief: y = 5x + 9
Officer: y= 8x + 0

Step 4. Set the lines equal to each other and solve for x. This is because the point at which they intersect will be the same point for both lines, so if you find x you can put that value in either equation to find the value for y. 

y = 5x + 9 and y = 8x + 0
5x + 9 = 8x + 0
    -9       -9

5x = 8x -9
-8x  -8x

-3x = -9
/-3   /-3

x = -9/-3
x = 3

Then plug in the x value into either of the equations:

y = 5x + 9     or     y = 8x + 0
y = 5(3)+9     or     y = 8(3)+0
y = 15 + 9     or     y = 24 + 0
y = 24         or     y = 24

Step 5. Analyze your results.

The point that you end up with is x = 3, y = 24 or (3,24). Since the y-axis is how many meters were traveled, and the x-axis is how many seconds. That means that in 3 seconds, the officer would have caught up to the thief. As well, we can tell that the officer caught the thief 24 meters away from the starting point.