Related Rates A police officer is standing near a highway using a radar gun. He
ID: 2852505 • Letter: R
Question
Related Rates
A police officer is standing near a highway using a radar gun. He aims the gun at a car that has just passed his position and when the gun is pointing at an angle of 45degrees to the direction of the highway, and notes that the distance between the car and the gun s increasing at a rate of 100km/h. How fast is the car travelling?
If another passing car is travelling at 90km/h along the straight highway, what will be the reading on the radar gun when the radar gun is aimed at 30 degrees to the highway?
Explanation / Answer
1) by pythogorus theorem
c2=a2+b2
differentiate with respect to time
2cdc/dt =2a da/dt +2b db/dt
da/dt=0 as it is constant
2cdc/dt = 0+2b db/dt
cdc/dt = b db/dt
db/dt =(c/b)dc/dt
db/dt =(2 x/ x)*100
db/dt =141.4 km/h
car travelling at 141.4 km/h
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reading on the radar gun when the radar gun is aimed at 30 degrees to the highway
=90 cos30o
=903 /2
=77.94
=78km/h