A helicopter takes off along the vertical with an acceleration a = 3 $m / s^{2}$ and zero initial velocity. In a certain time $t_{1}$ , the pilot switches off the engine. At the point of take off sound dies away in 30 sec. Find the velocity of helicopter at the moment when its engine is switched off. Take velocity of sound 320 m/s.

50 \sqrt{2}

m/s

No worries! We‘ve got your back. Try BYJU‘S free classes today!

60

m/s

No worries! We‘ve got your back. Try BYJU‘S free classes today!

40 \sqrt{2}

m/s

No worries! We‘ve got your back. Try BYJU‘S free classes today!

80

m/s

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is D $80$ m/s

Total time = $t_{1}$ + Time taken by sound to travel
$\Rightarrow 30 = t_{1} + \frac{\frac{1}{2} 3 t_{1}^{2}}{320}$
$(30 - t_{1}) 320 = \frac{3}{2} t_{1}^{2}$
$3 t_{1}^{2} + 640 t_{1} - 19200 = 0$
$t_{1} = 26.66$
$\Rightarrow v = 3 \times t = 3 \times 26.66 = 80 m / s$

Suggest Corrections

Similar questions

Q. A helicopter takes off along the vertical with an acceleration a = 3

m / s^{2}

and zero initial velocity. In a certain time

t_{1}

, the pilot switches off the engine. At the point of take off sound dies away in 30 sec. Find the velocity of helicopter at the moment when its engine is switched off. Take velocity of sound 320 m/s.

The mass of a helicopter is 0.5 t. Its engine develops a force of 8500 N before taking off. What is the acceleration of the helicopter at the time of taking off? (Give your answer in ms^-2)

___

Q. The retardation experienced by a moving motor boat after its engine is cut off, is given by

\frac{d v}{d t} = - 8 v^{2}

. If the magnitude of velocity at cut off is

v_{0} = 3 m/s

, the magnitude of the velocity

1 sec

after the cut off is (in

m/s

)

Q. The graph describes an airplane's acceleration

(a)

-time

(t)

during its take-off run. The airplane's velocity when it lifts off at

t = 20 s

is.

A firecracker has a sound intensity od 145 dB, which is exactly an average of sound intensities of jet engine at take off and fighter jet launch. Calculate the required scales for jet engine at take off and fighter jet.

Join BYJU'S Learning Program

The correct option is D 80 m/s Total time = t1 + Time taken by sound to travel ⇒30=t1+123t21320 (30−t1)320=32t21 3t21+640t1−19200=0 t1=26.66 ⇒v=3×t=3×26.66=80 m/s