Projectile Motion ：練習問題

An object is launched into the air at an angle. If air resistance is negligible, what is the direction of its acceleration at all points during its flight (after launch and before landing)?

A projectile is launched from level ground with an initial velocity. It reaches a maximum height of $$H_{\text{max}}$$ and has a horizontal range of $$R$$. During its flight, it passes through a point with horizontal displacement $$x$$ and vertical height $$y$$ (where $$0 < x < R$$ and $$0 < y < H_{\text{max}}$$). Which of the following expressions correctly relates $$x$$, $$y$$, $$R$$, and $$H_{\text{max}}$$? Assume air resistance is negligible and $$g$$ is the acceleration due to gravity.

A ball is thrown horizontally from the top of a building. Which of the following statements about its vertical motion is correct, neglecting air resistance?

For a projectile launched at an angle above the horizontal, which of the following statements is true at its highest point (ignoring air resistance)?

A stone is dropped from a certain height. At the same instant, another stone is projected horizontally from the same height with an initial velocity. Assuming no air resistance, which stone hits the ground first?

A projectile is launched from the ground at an angle of projection. Neglecting air resistance, identify the position in its trajectory where the speed of the projectile is at its minimum.

Determine the launch angle \(\theta\) (relative to the horizontal) for which the maximum height of a projectile is exactly equal to its horizontal range on level ground. (Neglect air resistance).

A ball is kicked from the top of a building of height \(20.0 \text{ m}\) with an initial velocity of \(15.0 \text{ m s}^{-1}\) at an angle of \(35.0^\circ\) above the horizontal. Calculate the horizontal distance from the base of the building to the point where the ball hits the ground. (Neglect air resistance and take \(g = 9.81 \text{ m s}^{-2}\).)

An arrow is fired from ground level with an initial speed of \( 25 \text{ m s}^{-1} \) at an angle of \( 30^\circ \) above the horizontal.
(a) Calculate the horizontal and vertical components of the initial velocity.
(b) State the velocity of the arrow (magnitude and direction) at its maximum height.
(c) Briefly explain why the horizontal component of the velocity remains constant throughout the flight if air resistance is ignored.

A supply package is dropped from a rescue plane flying horizontally at a constant speed of \( 80 \text{ m s}^{-1} \) and at a height of \( 500 \text{ m} \) above the level ground. Air resistance is negligible. Let \( g = 9.81 \text{ m s}^{-2} \).

(a) Explain why the horizontal velocity of the package remains constant during its fall. (1 mark)
(b) Calculate the time taken for the package to reach the ground. (2 marks)
(c) Find the horizontal distance between the point where the package was released and the point where it hits the ground. (1 mark)
(d) Calculate the magnitude of the velocity of the package just before it impacts the ground. (3 marks)
(e) If the plane's speed were doubled while the height remained the same, how would the time taken to reach the ground change? Briefly justify your answer. (1 mark)