$(i)$ How do bats make use of ultrasonic waves to catch their prey? Explain.
$(ii)$ $A$ radar signal is reflected by an aeroplane and is received $2 \times 10^{-5} \text{ s}$ after it was sent. If the speed of these waves is $3 \times 10^{8} \text{ m s}^{-1}$,how far is the aeroplane?

(N/A) $(i)$ Bats emit high-frequency ultrasonic waves. These waves strike the prey and reflect back to the bat. By analyzing the time delay and the nature of the reflected echoes,the bat can accurately determine the location,distance,and movement of its prey.
$(ii)$ Given:
Speed of radio waves $(v)$ $= 3 \times 10^{8} \text{ m s}^{-1}$
Total time taken $(t_{total})$ $= 2 \times 10^{-5} \text{ s}$
Since the signal travels to the aeroplane and back,the time taken to reach the aeroplane $(t)$ is half of the total time:
$t = t_{total} / 2 = (2 \times 10^{-5} \text{ s}) / 2 = 1 \times 10^{-5} \text{ s}$
Distance $(d)$ $=$ Speed $\times$ Time
$d = (3 \times 10^{8} \text{ m s}^{-1}) \times (1 \times 10^{-5} \text{ s})$
$d = 3 \times 10^{3} \text{ m} = 3000 \text{ m} = 3 \text{ km}$
Thus,the aeroplane is $3 \text{ km}$ away.