A sound transmitter and a projectile launcher are co-located at a distance of 210\text{ m}… — JAMB UTME

A sound transmitter and a projectile launcher are co-located at a distance of $210\text{ m}$ directly in front of a tall, flat vertical cliff. At time $t = 0\text{ s}$ , a projectile is launched directly away from the cliff at a constant speed of $60\text{ m s}^{-1}$ , while a sound pulse is emitted simultaneously towards the cliff. The sound wave reflects off the cliff face and travels back to overtake the moving projectile. Assuming the speed of sound in air is $340\text{ m s}^{-1}$ , calculate the distance from the cliff face, in meters, to the position where the reflected sound wave intercepts the projectile.

Cevap: 300 m

Cevap

The distance of the projectile from the cliff face at the instant of interception is

300\text{ m}

The correct calculation accounts for both the two-part path of the sound wave (forward to cliff + back to projectile) and the displacement of the projectile moving away from the cliff over the same time interval, yielding an interception distance of

300\text{ m}

from the cliff.

Adım Adım Çözüm

Set up the total distance expression for the sound wave from the cliff face

Total sound path =

210\text{ m} + x

The sound pulse must travel

210\text{ m}

forward to hit the cliff face, plus an additional distance

x

away from the cliff face after reflection to reach the projectile.

Set up the distance expression for the projectile from its starting point

Projectile path =

x - 210\text{ m}

The projectile starts

210\text{ m}

away from the cliff and moves farther away to position

x

Equate the time elapsed for both sound propagation and projectile movement

\frac{210 + x}{340} = \frac{x - 210}{60}

Both events happen simultaneously over the exact same time interval

t

Solve the linear equation for

x

x = 300\text{ m}

Cross-multiplying yields

60(210 + x) = 340(x - 210)

, which simplifies to

28x = 8400

, giving

x = 300\text{ m}

Anahtar Kavram

Echo reflection path combined with relative linear kinematics

Soru

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