A boy on a bicycle approaches a brick wall as he sounds his horn at a frequency 400 Hz. The sound he hears reflected back from the wall is at a frequency 408 Hz. At what speed is the boy riding his bicycle toward the wall

6.8 m/s

Explanation:

To solve this, we would use the Doppler's Effect. Doppler's effect is represented by the formula

f = [(g + vr)/(g + vs)].fo, where

f = observed frequency, 408 Hz

g = speed of sound in air, 340 m/s

vr = velocity of the receiver

vs = velocity of the source, 0 m/s

fo = source frequency, 400 Hz

Now, applying the values to the equation, we have

408 = [(340 + vr)/(340 + 0) * 400

408/400 = (340 + vr)/340

1.02 * 340 = 340 + vr

346.8 = 340 + vr

vr = 346.8 - 340

vr = 6.8 m/s

Therefore the speed at which the boy is riding his bicycle towards the wall is 6.8 m/s

no. dot product   =0 when vecs at right angles