(I) A hiker determines the length of a lake by listening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.5 s after shouting. Estimate the length of the lake.

425 m

Explanation:

From the question,

v = 2x/t Equation 1

Where v = speed of sound in air, x = Length of the lake, t = time.

make x the subject of the equation

x = vt/2 Equation 2

Given: t = 2.5 s

Constant: v = 340 m/s.

Substitute these values into equation 2

x = 340(2.5)/2

x = 425 m.

Hence the length of the lake is 425 m

c. magnitude and direction