Question

a projectile is launched at some angle to the horizontal with some initial speed (v_{i}), and air resistance is negligible. (a) is the projectile a freely - falling body? yes no (b) what is its acceleration in the vertical direction? (let up be the positive direction.) (m/s^{2}) (c) what is its acceleration in the horizontal direction? (m/s^{2}) resources read it

Explanation:

Step1: Define freely - falling body

A freely - falling body has only the force of gravity acting on it. The projectile has only gravitational force acting on it (since air resistance is negligible), so it is a freely - falling body.

Step2: Determine vertical acceleration

The only force in the vertical direction is gravity. The acceleration due to gravity near the Earth's surface is approximately $g=- 9.8\ m/s^{2}$ (negative because the positive direction is up and gravity acts downwards).

Step3: Determine horizontal acceleration

There is no horizontal force acting on the projectile (no air resistance). According to Newton's second law $F = ma$, with $F_x = 0$, the horizontal acceleration $a_x=0\ m/s^{2}$.

Answer:

(a) Yes
(b) $-9.8$
(c) $0$