With what acceleration will a 0.5 kg ball under water float if the force of gravity acting on it is 5 Newtons

With what acceleration will a 0.5 kg ball under water float if the force of gravity acting on it is 5 Newtons, the Archimedean force is 10 Newtons, and the average force of resistance to motion is 2 Newtons?

m = 0.5 kg.

g = 9.8 m / s ^ 2.

Ft = 5 N.

Farch = 10 N.

Fcopr = 2 N.

a -?

3 forces act on the body: gravity Ft directed vertically downward, buoyancy force of Archimedes Farch directed vertically upward, force of resistance to motion Fcopr directed vertically downward.

Let’s write Newton’s 2 law in vector form: ma = Ft + Farch + Fcopr.

We direct the OU axis vertically upward and write 2 Newton’s law in projections onto it: m * a = Farch – Fcopr – Ft.

a = (Farch – Fcopr – Ft) / m.

a = (10 N – 2 N – 5 N) / 0.5 kg = 6 m / s ^ 2.

Answer: the acceleration of the body is a = 6 m / s ^ 2.