Question

Suppose that the distance an aircraft travels along a runway before takeoff is given by Upper D equals (5 divided by 3 )t squared​, where D is measured in meters from the starting point and t is measured in seconds from the time the brakes are released. The aircraft will become airborne when its speed reaches 480 km divided by h. How long will it take to become​ airborne, and what distance will it travel in that​ time? How long will the airplane take to become​ airborne?

Answer 1

40 seconds

2666.66 m

Step-by-step explanation:

t = Time taken

u = Initial velocity

v = Final velocity

s = Displacement

a = Acceleration

`D=(5)/(3)t^2`

`s=ut+(1)/(2)at^2\\\Rightarrow D=0t+(1)/(2)* a* t^2\\\Rightarrow D=(1)/(2)at^2`

Equating the two equations

`(5)/(3)t^2=(1)/(2)at^2\\\Rightarrow a=(5)/(3)* (2)/(1)=(10)/(3)\ m/s^2`

`v=u+at\\\Rightarrow t=(v-u)/(a)\\\Rightarrow t=((480)/(3.6)-0)/((10)/(3))\\\Rightarrow t=40\ s`

Time taken by the plane to get airborne is 40 seconds

`v^2-u^2=2as\\\Rightarrow s=(v^2-u^2)/(2a)\\\Rightarrow s=((480)/(3.6)^2-0^2)/(2* (10)/(3))\\\Rightarrow s=2666.67\ m`

Distance the plane has to travel to get airborne is 2666.66 m