A police car is located 70 feet to the side of a straight road. A red car is driving along the road in the direction of the police car and is 160 feet up the road from the location of the police car.

Question

A police car is located 70 feet to the side of a straight road. A red car is driving along the road in the direction of the police car and is 160 feet up the road from the location of the police car. The police radar reads that the distance between the police car and the red car is decreasing at a rate of 75 feet per second. How fast is the red car actually traveling along the road? The actual speed (along the road) of the red car is _______ feet per second

Please, I need help with this question.

Answer 1

red car is going about 81.86 ft/sec

let distance between the police and red cars = h

distance from the red car to a point horizontal to the police car = a

distance from from the road to the police car = b

h^2 = a^2 + b^2

take the derivative with respect to time

hh' = aa' + bb' b'=0

174.64(75) = 160a'

a' = 174.64(75)/160 = 81.86

81.86 ft/sec = 81.86(5280)/60^2 = about 120.06 mph

1 mile = 5280 feet

1 hour = 60 minutes x 60 seconds = 3600 seconds

1 mile per hour = 5280 feet per 3600 seconds

1 foot per second = 5280/3600 mph = 1.4666...mph

81.86 x 1.4666... = 120.061333...

an arrest for reckless driving, maybe felony endangerment is about to happen, with radar evidence enough to convince any jury, unless it wasn't calibrated properly or failed quality assurance tests. The prosecutor and police may hide any evidence that discredits that radar results though. Some jail time is likely, unless no prior driving problems or criminal record. if the red car driver doesn't believe he was going 120 mph, his attorney should make a motion for disclosure of everything about the radar and officer. There may be similar cases where he falsely arrested drivers for speeding based on faulty radar or his own need to fill a quota or tickets or arrests. Worse than jail or possible prison is the suspended maybe revoked drivers license plus huge fine and huge increase in insurance premiums if you can get any insurance.

Take a square with 4 sides each = s = 24 m

a circle inside with radius = 5

the area between the square and circle = s^2 - pir^2

take the derivative with respect to time

A' = 2ss' - 2pirr' = 2(24)(-4) - 2pi(5)(2) = -192 - about 62.8318 = about -129.1682 m^2/hour