Question

A jet aircraft with mass of 658,055 kilograms is flying straight downward. At an instant the plane's engine is producing an downward thrust (force) of 1,484,732.5 Newtons and air resistance is exerting a force of 740,492.6 Newtons upward. What is the acceleration of the plane in m/s2 at that instant?

Answer 1

The acceleration of the plane is 10.93 m/s² at that instant.

Step-by-step explanation:

Given:

Mass of aircraft,
`m=658055\textrm{ kg}`

Downward thrust produced,
`F=1484732.5\textrm{ N}`

Upward resistance force by air,
`F_(R)=740492.6\textrm{ N}`

Weight of the aircraft acting donward,
`W=mg=658055* 9.8=6448939\textrm{ N}`

According to Newton's second law, net force acting on an object is equal to the product of mass and its acceleration.

Here, the net force is given as the difference of downward forces and upward forces.

`F_(net)= F+W-F_(R)\\ F_(net)=1484732.5+6448939-740492.6=7193178.9\textrm{ N}`

Now,

`F_(net)=ma\\7193178.9=658055a\\a=(7193178.9)/(658055)=10.93\textrm{ }m/s^(2)`

Therefore, the acceleration of the plane is 10.93 m/s² at that instant.