Question

A police car notices a speeding car travelling at 60 ft/s East, 5 s after it passes the intersection. The police gives chase immediately, and they start off 650 ft South of the intersection. The police car will run with a velocity of 80 ft/s, going North.

Answer 1

Answer: it will take the police car 25 seconds and 2000 feet to catch up with the speeding car.

Step-by-step explanation: To determine the distance and time that the police car needs to catch up with the speeding car, we can set up the following system of equations:

Let x be the time it takes for the police car to catch up with the speeding car

Let y be the distance the police car needs to travel to catch up with the speeding car

The distance the speeding car travels in x seconds is given by the equation:

60x = distance

The distance the police car travels in x seconds is given by the equation:

80x = y

The distance between the two cars at the start is given by the equation:

(y - 650)^2 + 650^2 = x^2

We can solve this system of equations by substituting the second equation into the third equation, resulting in:

(80x - 650)^2 + 650^2 = x^2

Expanding and rearranging the terms, we get:

6400x^2 - 19600x + 422500 = x^2

Solving for x, we get:

x = 25 seconds

Substituting this value back into the equation for the distance the police car travels, we get:

y = 80 * 25 = 2000 ft

Answer 2

To find out how long it will take for the police car to catch up to the speeding car, you can use the following formula:

t = d / v

Where t is the time it takes to catch up, d is the distance between the police car and the speeding car, and v is the relative speed of the police car compared to the speeding car.

In this case, the distance between the police car and the speeding car is given by the Pythagorean theorem:

d = sqrt((650 ft)^2 + (60 ft/s * 5 s)^2) = 674.22 ft

The relative speed of the police car compared to the speeding car is given by:

v = 80 ft/s - 60 ft/s = 20 ft/s

Plugging these values into the formula, we get:

t = d / v = 674.22 ft / 20 ft/s = 33.71 s

So it will take the police car approximately 33.71 seconds to catch up to the speeding car.

Note: This is just an approximation and the actual time required may vary depending on the exact positions and speeds of the two cars