A radio station's signal has a radius of 100 miles. If you drive at a constant speed of 40 miles an hour, nonstop, directly across the diameter of the signal, how long can you listen to the station before the signal fades?

The radius is 100 miles . . . so the diameter is 200 miles (100 miles towards the transmitter and 100 miles going away.

At 40mph it takes 5 hours to drive 200 miles, therefore you could listen to the station for 5 hours.

Answer Link

johanrusli johanrusli · Answer 2 · 2019-10-30T04:22:18-04:00

You can listen to the station for 5 hours before the signal fades

Further explanation

Acceleration is rate of change of velocity.

\(\large {\boxed {a = \frac{v - u}{t} } }\)

\(\large {\boxed {d = \frac{v + u}{2}~t } }\)

a = acceleration ( m/s² )

v = final velocity ( m/s )

u = initial velocity ( m/s )

t = time taken ( s )

d = distance ( m )

Let us now tackle the problem!

Given:

Radius of Signal = R = 100 miles

Speed of Car = v = 40 miles/hour

Unknown:

Time Taken = t = ?

Solution:

\(\texttt{Time Taken} = \texttt{Distance} \div \texttt{Speed of Car}\)

\(\texttt{Time Taken} = \texttt{Diameter of Signal} \div \texttt{Speed of Car}\)

\(\texttt{Time Taken} = \texttt{2 x Radius of Signal} \div \texttt{Speed of Car}\)

\(\texttt{Time Taken} = 2 \times 100 \div \texttt{40}\)

\(\texttt{Time Taken} = 200 \div 40\)

\(\texttt{Time Taken} = 5 \texttt{ hours}\)

Learn more

Velocity of Runner : https://brainly.com/question/3813437
Kinetic Energy : https://brainly.com/question/692781
Acceleration : https://brainly.com/question/2283922
The Speed of Car : https://brainly.com/question/568302

Answer details

Grade: High School

Subject: Physics

Chapter: Kinematics

Keywords: Velocity , Driver , Car , Deceleration , Acceleration , Obstacle , Signal , Radio , Station , Fade , Nonstop