Calculus Officer: Ticket or No Ticket?

[ldbaseball16]

Homework Statement

The calculus Radar Intercept Officer is standing on a bridge over the highway and taking readings on the incoming traffic. His radar gun is 25 feet above the highway. When a vehicle crosses a painted line which is 50.00 feet from the point on the highway directly below the radar gun, the gun reads 66.0 miles per hour. The speed limit is 70 miles per hour. Ticket or no Ticket?
(I have no idea where to begin can someone point me in a direction please and thank you)

Homework Equations

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3. The Attempt at a Solution [/b
I don't know where to start

 

[mighty2000]

with this problem. Can someone please guide me in the right direction?

Hello,

I would approach this problem by first understanding the given information and identifying what is being asked. The radar gun is 25 feet above the highway and reads 66.0 miles per hour when a vehicle crosses a painted line 50.00 feet away from the gun. The speed limit is 70 miles per hour, and the question is whether or not to issue a ticket.

To solve this problem, we can use the equation for speed, which is distance divided by time. We know the distance the radar gun is from the painted line (50.00 feet) and the speed it reads (66.0 miles per hour). However, we need to convert the distance and speed to the same units, so let's convert 66.0 miles per hour to feet per second.

1 mile = 5,280 feet
1 hour = 3,600 seconds

66.0 miles per hour x (5,280 feet/1 mile) x (1 hour/3,600 seconds) = 97.2 feet per second

Now, we can use the equation for speed to find the time it takes for the vehicle to travel 50.00 feet.

Speed = Distance/Time
97.2 feet per second = 50.00 feet/Time
Time = 50.00 feet/97.2 feet per second = 0.514 seconds

This means that the vehicle took 0.514 seconds to travel 50.00 feet. Now, we can use this time to calculate the actual speed of the vehicle.

Speed = Distance/Time
Speed = 50.00 feet/0.514 seconds = 97.2 feet per second

We can now convert this speed to miles per hour to compare it to the speed limit.

1 mile = 5,280 feet
1 hour = 3,600 seconds

97.2 feet per second x (1 mile/5,280 feet) x (3,600 seconds/1 hour) = 66.0 miles per hour

We can see that the actual speed of the vehicle is 66.0 miles per hour, which is the same as the reading on the radar gun. Since the speed limit is 70 miles per hour, the vehicle is not exceeding the speed limit and therefore, no ticket should be issued.

I hope this helps guide you in the right