Question textFor a projectile its Answer 1 Question 4[select: , height, horizontal velocity component, vertical velocity component, velocity vector] is the same at all points on its path.As well as this, its Answer 2 Question 4[select: , speed, acceleration vector, horizontal acceleration component, vertical acceleration component] is constant at all times it is in the air.

Question

BlackTom AI · Accepted Answer

Horizontal velocity component is constant because the horizontal acceleration is zero (assuming no air resistance) and the acceleration vector is constant because gravity provides a steady, uniform acceleration downward.

1) Relevant concepts
- Decompose motion into horizontal (x) and vertical (y) components. Projectile motion with negligible air resistance is driven only by gravity.
- Horizontal acceleration ax = 0, vertical acceleration ay = −g (g ≈ 9.8 m/s^2). The acceleration vector a = (0, −g) is therefore constant in both magnitude and direction.

2) Step-by-step reasoning and equations
- Write the initial velocity components: v0x = v0 cosθ, v0y = v0 sinθ.
- Horizontal velocity as a function of time: vx(t) = v0x = v0 cosθ. This shows vx does not depend on time, so it is the same at all points on the path.
- Vertical velocity as a function of time: vy(t) = v0y − g t = v0 sinθ − g t, which changes with time.
- Acceleration components: ax(t) = 0, ay(t) = −g. Therefore the acceleration vector a(t) = (0, −g) for all t while the projectile is in flight.

3) Intermediate steps / small calculation
- Example: if v0 = 20 m/s and θ = 30°, v0x = 20 cos30° ≈ 17.32 m/s. For any time t, vx(t) = 17.32 m/s (unchanged).
- vy at t = 1 s: vy = 20 sin30° − 9.8·1 = 10 − 9.8 = 0.2 m/s (different from initial vy).

4) Why the correct answers are correct
- Horizontal velocity component is constant because there is no horizontal acceleration to change it.
- The acceleration vector is constant because gravity provides a constant downward acceleration (same magnitude and direction throughout the flight).

5) Why other options are incorrect (brief)
- Speed is not constant: speed changes because the vertical component changes.
- Vertical velocity component is not constant: it changes linearly with time due to −g.
- Velocity vector is not the same at all points: its direction and magnitude change.
- Height varies along the trajectory (except trivial endpoints).

Conclusion: The horizontal velocity component is the same at all points, and the acceleration vector is constant while the projectile is in the air. This confirms the provided answers: "horizontal velocity component" and "acceleration vector."

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