Question

The velocity of a projectile at launch has a horizontal component vh and a vertical component vv. When the projectile is at the highest point of its trajectory, identify the vertical and the horizontal components of its velocity and the vertical component of its acceleration. Consider air resistance to be negligible

Answer 1

Answer:

- horizontal component of the velocity: $v_h$ (because it is constant)

- vertical component of the velocity: 0

- vertical component of the acceleration: $-g=-9.8 m/s^2$ (downward)

Explanation:

The motion of a projectile consists of two independent motions:

- Along the horizontal direction, there are no forces acting on the projectile (if we neglect air resistance), therefore the horizontal acceleration is zero and the horizontal component of the velocity, vh, is constant

- Along the vertical direction, there is only one force acting on the projectile: the force of gravity, downward, which produces a constant downward acceleration of $g=9.8 m/s^2$. As a consequence, the vertical component of the velocity changes according to

$v_v(t) = v_v-gt$

where vv is the initial vertical velocity and t the time. According to this equation, the vertical component of the velocity decreases first, then becomes zero at the point of maximum height, then becomes negative (= changes direction and points downward)

So, in summary, at the highest point of the trajectory we have:

- horizontal component of the velocity: $v_h$ (because it is constant)

- vertical component of the velocity: 0

- vertical component of the acceleration: $-g=-9.8 m/s^2$ (downward)