3. You toss a ball at an angle 45° above the horizontal. After the ball leaves your hands, its

motion can be described in terms of displacement,

velocity, and acceleration. For each item, is the

quantity constant, changing linearly, or changing

nonlinearly during consecutive time intervals?

horizontal displacement

horizontal velocity

horizontal acceleration

vertical displacement

vertical velocity

vertical acceleration

LINEARLY CHANGE horizontal displacement

CONSTANT horizontal speed

CONSTATE EQUAL TO ZERO horizontal acceleration

NON-LINEAR vertical displacement is quadratic

LINEARLY CHANGE vertical speed

CONSTATE EQUAL TO g vertical acceleration

Explanation:

The launch of projectiles is analyzed in the form of two independent movements connected by a scalar which is time.

In the vertical part of the movement it is affected by the acceleration of gravity and in the horizontal movement there is no acceleration, neglecting air resistance.

The equations of vertical motion are

          y = y₀ - gt

          y = y₀ + t - ½ g t²

the equations for horizontal motion are

         vₓ = x / t

now we can answer the questions

LINEARLY CHANGE horizontal displacement

CONSTANT horizontal speed

CONSTATE EQUAL TO ZERO horizontal acceleration

NON-LINEAR vertical displacement is quadratic

LINEARLY CHANGE vertical speed

CONSTATE EQUAL TO g vertical acceleration

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