Question

. An aircraft travelling at 600 km/h accelerates steadily at 10 km/h per second. Taking the speed of sound as 1100 km/h at the aircraft’s altitude, how long will it take to reach the ‘sound barrier’ ?

Answer 1

Answer:

50 seconds.

Explanation:

The acceleration of aircraft in km/h²

$10\frac{km}{h\ s}=10\frac{km}{h\ \frac{1}{3600}h}=36000\frac{km}{h^2}$

Now, to cross sound barrier,

final velocity, $v$ = 1100 km/h

initial velocity, $u$ = 600 km/h

acceleration, $a$ = 36000 km/h²

So, according to the formula $v=u+at$

$t=\frac{v-u}{a}\\\\t=\frac{1100-600}{36000}\\\\t=\frac{500}{36000}\\\\t=\frac{5}{360} hour\\\\t=50\,seconds$

Answer 2

Explanation:

The acceleration of aircraft in km/h²

10\frac{km}{h\ s}=10\frac{km}{h\ \frac{1}{3600}h}=36000\frac{km}{h^2}10

h s

km

=10

h

3600

1

h

km

=36000

h

2

km

Now, to cross sound barrier,

final velocity, vv = 1100 km/h

initial velocity, uu = 600 km/h

acceleration, aa = 36000 km/h²

So, according to the formula v=u+atv=u+at

\begin{lgathered}t=\frac{v-u}{a}\\\\t=\frac{1100-600}{36000}\\\\t=\frac{500}{36000}\\\\t=\frac{5}{360} hour\\\\t=50\,seconds\end{lgathered}

t=

a

v−u

t=

36000

1100−600

t=

36000

500

t=

360

5

hour

t=50seconds