The flight range of a body thrown in a horizontal direction at a speed of v = 10 m / s

The flight range of a body thrown in a horizontal direction at a speed of v = 10 m / s is equal to the throwing height (l = h). Neglect air resistance. From what height h is the body thrown?

The movement of a body thrown at an angle to the horizon can be viewed as a superposition of two independent movements: uniformly accelerated vertical movement and uniform horizontal movement.

Since the body is thrown horizontally, the vertical projection of its velocity is zero (vy = 0). For such uniformly accelerated vertical movement, you can write:

h = g * t ^ 2/2.

Since the body is thrown horizontally, the horizontal projection of its speed is equal to its full speed (vx = v) and it does not change with time. For such a uniform horizontal movement, you can write:

l = v * t.

By hypothesis, h = l, therefore

g * t ^ 2/2 = v * t,

whence the flight time of the body is

t = 2 * v / g.

Then the required height h is equal to

h = g * t ^ 2/2 = g * (2 * v / g) ^ 2/2 = 2 * v ^ 2 / g;

h = 2 * 10 ^ 2/10 = 20 m.