During projectile motion, which of the following quantities remains constant? (ignoring air resistance).

Question

BlackTom AI · Accepted Answer

Horizontal acceleration is zero while vertical acceleration equals -g, so the acceleration vector is constant and the horizontal component of velocity remains constant (ignoring air resistance).

1) Relevant knowledge points and concepts
- Projectile motion (near Earth's surface, no air resistance) separates into independent horizontal and vertical motions.
- Gravity provides a constant downward acceleration g (≈9.8 m/s^2). Thus the acceleration vector a = (0, -g) is constant in time.
- Horizontal motion has no horizontal force → horizontal acceleration ax = 0 → horizontal velocity vx is constant.
- Vertical velocity changes with time because ay = -g, so vy(t) = v0y − g t.
- Momentum p = m v changes if any component of v changes; kinetic energy depends on the speed |v| and therefore can change.

2) Complete reasoning, step by step
- Write acceleration components: ax = 0, ay = −g. Since both components are constant numbers, the acceleration vector a = (ax, ay) is constant.
- Integrate ax: dvx/dt = 0 → vx(t) = vx0 (constant).
- Integrate ay: dvy/dt = −g → vy(t) = vy0 − g t (varies with time).
- Therefore horizontal velocity is constant, vertical velocity is not.

3) Intermediate calculations (symbolic)
- ax = 0 → dvx/dt = 0 → vx(t) = vx(0) = v0x.
- ay = −g → dvy/dt = −g → vy(t) = v0y − g t.
- Speed v(t) = sqrt(vx^2 + vy(t)^2) so kinetic energy KE = 1/2 m v(t)^2 generally changes as vy(t) changes.

4) Why the correct answer is correct
Because acceleration vector (0, −g) does not change in time and the horizontal acceleration is zero, the horizontal velocity remains unchanged. Hence “acceleration and horizontal velocity” are the quantities that remain constant.

5) Why other options are incorrect
- a (acceleration and vertical velocity): vertical velocity is not constant (it changes as vy = v0y − g t).
- c (weight and momentum): weight (mg) is constant, but momentum changes because vy changes, so total momentum is not constant.
- d (weight and kinetic energy): weight may be constant, but kinetic energy changes as the vertical component of velocity changes.

Conclusion: The correct choice is b. acceleration and horizontal velocity, which matches the provided answer.

During projectile motion, which of the following quantities remains constant? (ignoring air resistance).单项选择题

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