Answer to Question #226623 in Mechanical Engineering for Papi Chulo

Question

A hovercraft stays off the ground by blowing air out underneath it. It can accelerate (forwards or backwards) at 0,6 m/s²Â by blowing air with a steering fan (backwards or forwards). If the hovercraft is moving forwards at 12 m/s and the steering fan is suddenly turned to accelerate the hovercraft backwards, calculate:

a) the velocity of the hovercraft after 2 s

b) the time it takes for the hovercraft to reach zero velocity 

c) the velocity of the hovercraft after 29 s

d) the displacement of the craft when it has zero velocity

e) the displacement of the hovercraft when it is moving backwards at 16m/s

f) Clearly show what the value of h(max),t(total) and v

State whether the hovercraft is going backwards or forwards after each question’s answer.

(Make forward direction positive and backwards direction negative)

Answer 1

Part (a)

we have to find velocity after 2sec is:

$v=u+at\\ v=12-0.6*2=10.8m/s$

(here a=-0.6m/s^2 because the hovercraft suddenly start moving backward)

Part (b)

we have to find time taken by hovercraft when its velocity become zero:

using same formula:

$v=0,u=12m/s,a=-0.6m/s^2$

$so, t=20sec$

Part (c)

velocity after 29sec is:

$v=12-(0.6*29)=2.6m/s$

Part (d)

displacement when velocity becomes zero:

$v^2=u^2+2as\\ s=\frac{(u^2)}{2a}=\frac{(12*12)}{(2*.6)}=120m$

Part (e)

displacement when it is moving backward at velocity 16m/s

$so s=\frac{(v^2-u^2)}{2a}\\ s=\frac{(16*16-12*12)}{(2*0.6)}=93.3m$

Part(f)

$v=u+at$ (1st eqaution of motion)

$v=0,u=12m/s and a=-0.6$

therefore,$t=20sec$ (time of going upward)

hence, total time of flight is $2*20=40 sec$

$h_{max}=\frac{(u^2)}{2a}=\frac{(12*12)}{(2*.6)}=120m$

$v= \frac{s}{t}=\frac{120}{40}= 3 m/s$