Question

a helicopter takes off along the vertical with an acceleration of 3 m/s^2 and zero initial velocity in a certain time the pilot features of the engine at the time of take off the sound dies away in 30 sec .determine the velocity of a helicopter at the moment when its engine is switched off assuming the velocity of sound is 320 m/s

Answer 1

Hello Dear.

Here is the answer---

Given Conditions ⇒

Acceleration (a) = 3 m/s².
Initial velocity (u) = 0.

Speed of the sound in air = 320 m/s.
Time = 30 s.

Using the Formula,

Speed = Distance/Time
Distance = Speed × Time
⇒ Distance = 320 × 30
⇒ Distance = 9600 m.
∴ Distance traveled by the sound is 9600 m.

Now, Using the Equation of Motion,

v² - u² = 2aS

⇒ v² - (0)² = 2 (3)(9600)
⇒ v² = 57600
Taking square root on both sides,
v = √57600
v = 240 m/s.

Thus, the Velocity of the Helicopter when the engine is awitched off is 240 m/s.


Hope it helps.

Answer 2

Intial velocity of helicopter , u = 0
helicopter takes off along vertical with an acceleration of 3 m/s²
Hence, acceleration act on helicopter, a = 3 m/s²

Distance travelled by sound in 30 second = distance travelled by helicopter
= speed of sound × time taken
= 320 × 30 m

Now, use formula
V² = u² + 2aS
⇒v² = 0 + 2 × 3 × 320 × 30
⇒v² = 6400 × 9
taking square root both sides,
v = 240 m/s

Hence, answer should be 240 m/s