At what point in time is the tangential acceleration equal to normal for a body thrown horizontally

At what point in time is the tangential acceleration equal to normal for a body thrown horizontally with an initial velocity v0 = 20 m / s?

Data: V0 – initial horizontal throw speed (V0 = 20 m / s).

Const: g – acceleration due to gravity (g ≈ 10 m / s2).

To find out the required time from the moment of the start of the throw, we use the equality: an = V0 * g / √ (V0 ^ 2 + g ^ 2 * t ^ 2) = aτ = g ^ 2 * t / √ (V0 ^ 2 + g ^ 2 * t ^ 2).

The transformed equality: V0 = g * t, whence we express: t = V0 / g.

Let’s perform the calculation: t = V0 / g = 20/10 = 2 s.

Answer: The tangential acceleration of the indicated body will become equal to normal in 2 s.