The petard explodes 3 seconds after being thrown. How fast should it be thrown so that it explodes at the top

The petard explodes 3 seconds after being thrown. How fast should it be thrown so that it explodes at the top of the trajectory at a distance of at least 60 meters from the throwing point? Do not take air resistance into account, take the acceleration of gravity equal to 10 m / s ^ 2

t = 3 seconds – the time interval after which the firecracker explodes;

g = 10 m / s ^ 2 – acceleration of gravity;

L = 60 meters – the required distance from the throwing point to the firecracker.

It is required to determine v0 (m / s) – the speed that needs to be reported to the firecracker.

Since the problem statement is not specified, we assume that the throw is performed vertically upward. Then:

L = v0 * t – g * t ^ 2/2

v0 * t = L + g * t ^ 2/2

v0 = L / t + g * t / 2 = 60/3 + 10 * 3/2 = 20 + 5 * 3 = 20 + 15 = 35 m / s.

Answer: the firecracker needs to be told an initial speed of 35 m / s.