Apolice officer is chasing a purse-snatcher down a street. the thief
starts 9 meters ahead of the officer and can run 20 meters in 4 second
(5 m/s). the police officer can run 32 meters in 4 seconds (8 m/s). how long will it take the officer to catch the thief?

3 seconds

Explanation:

We can give an expression for the position of both the thief and of the police officer at time t.

The position of the thief at time t is given by

where 9 is its initial position in m and 5 is its speed in m/s.

Instead, the position of the police officer at time t is given by

where 0 is its initial position in m and 8 is its speed in m/s.

The police officer will catch the thief when their position will be equal, so

By solving,

magnityde and direction

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