1. Do alto de uma plataforma com 15m de altura, é lançado horizontalmente um projéctil. Pretende-se atingir um alvo localizado no solo, a 50m da vertical, que contém o ponto de lançamento.
a) Determine a velocidade inicial do lançamento;
b) Determine a velociade ao tocar o solo.

(a). The initial velocity is 28.58m/s

(b). The speed when touching the ground is 33.3m/s.

Explanation:

The equations governing the position of the projectile are

where is the initial velocity.

(a).

When the projectile hits the 50m mark, ; therefore,

solving for we get:

Thus, the projectile must hit the 50m mark in 1.75s, and this condition demands from equation (1) that

which gives

(b).

The horizontal velocity remains unchanged just before the projectile touches the ground because gravity acts only along the vertical direction; therefore,

the vertical component of the velocity is

which gives a speed of