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

The horizontal component of velocity remains constant because there is no horizontal acceleration (neglecting air resistance), and the acceleration vector is constant (gravity points downward with constant magnitude).

1) Relevant concepts
- Projectile motion separates into independent horizontal and vertical motions.
- Horizontal motion: no horizontal force ⇒ ax = 0 ⇒ horizontal velocity component vx is constant.
- Vertical motion: gravity provides constant downward acceleration ay = −g, so vertical velocity changes linearly with time.
- The acceleration vector a = (ax, ay) = (0, −g) is therefore a constant vector in time.

2) Step-by-step reasoning
- Write the velocity components for a projectile launched with initial speed u at angle θ:
  vx(t) = u cosθ (since ax = 0)
  vy(t) = u sinθ − g t (since ay = −g)
- These expressions show vx does not depend on t while vy does, so vx is the same at all points on the path.
- The acceleration components are ax = 0 and ay = −g, both constant in time, so the acceleration vector a(t) = 0 i − g j is constant.

3) Intermediate steps / equations
- v(t) = vx(t) i + vy(t) j = (u cosθ) i + (u sinθ − g t) j
- a(t) = dv/dt = 0 i − g j = constant

4) Why the correct answers are correct
- "Horizontal velocity component": vx = u cosθ is time-independent, so it is the same at all points.
- "Acceleration vector": a = (0, −g) does not change with time or position (ignoring air resistance), so the entire acceleration vector is constant while the projectile is in the air.

5) Why the other options are incorrect (brief)
- Height: changes throughout the flight (rises then falls).
- Vertical velocity component: changes with time due to ay = −g.
- Velocity vector: direction and magnitude change (vy changes), so it is not constant.
- Speed: magnitude of velocity changes because vy changes.
- Horizontal acceleration component: while ax = 0 is constant, this option is less complete than "acceleration vector" (which states the full vector is constant); the best correct choice is the acceleration vector.

6) Conclusion
The correct pair is "horizontal velocity component" and "acceleration vector", which matches the provided answers.

类似问题

A rock is thrown up through the air at an angle. Which of the following quantities is equal in size to its minimum speed?

A football player kicks a ball with an initial velocity of 25 m s-1 at an angle of 53° to the horizontal. The horizontal component of the initial velocity of the ball is

A baseball is hit with a velocity of 18.56 m/s of at an angle of 39.7° to the horizontal and returns to the same initial height.Calculate the time of flight in seconds.Give your answer to 2 decimal places without units.

A ball is projected horizontally from the top of a 30.8 m high cliff with a speed of 5 ms-1. Ignoring air resistance, how far from the base of the cliff will the ball land?

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

A baseball is hit with a velocity of 15.38 m/s of at an angle of 35.8° to the horizontal and returns to the same initial height.Calculate the time of flight in seconds.Give your answer to 2 decimal places without units.

A ball is projected horizontally from the top of a 31.1 m high cliff. The ball lands on the ground after travelling a horizontal range of 29.1 m.Ignoring air resistance, what was the initial velocity of the ball?

更多留学生实用工具

智能学习助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单