Question

A sack of potatoes weighing 16.0-kg falls from a very tall building. At a certain point at the motion downwards, its measured acceleration is 4.6 m/s2 and its velocity is 54.2 m/s. Assuming that the magnitude of the drag force due to air resistance is proportional to the square of its speed, What is its terminal speed?

Answer 1

The terminal speed is 74.833 m/s

Step-by-step explanation:

The drag force is equal to square of speed:

Fdrag = k*v²

According Newton`s law:

Fnet = m*a

m*g - k*v² = m*a

`k=(m(g-a))/(v^(2) )`

`k=(16*(9.8-4.6))/(54.2^(2) ) =0.028`

If terminal speed, the net force is zero.

`kv_(t) ^(2) =mg\\v_(t) =\sqrt{(mg)/(k) } =\sqrt{(16*9.8)/(0.028) } =74.833m/s`