拋體運動：練習題

A ball is projected horizontally from the top of a vertical cliff of height \(45\text{ m}\) with an initial horizontal speed of \(12\text{ m s}^{-1}\).
Assume air resistance is negligible and take the acceleration due to gravity as \(g = 9.81\text{ m s}^{-2}\).
What is the horizontal distance travelled by the ball before it hits the ground?

A stone is projected from ground level with a velocity of \(20\text{ m s}^{-1}\) at an angle of \(40^\circ\) above the horizontal.
What is the speed of the stone at its maximum height? Neglect air resistance.

A projectile is launched from ground level at an angle \(\theta\) above the horizontal with initial kinetic energy \(E_k\).
At the highest point of its trajectory, its kinetic energy is measured to be \(\frac{1}{4} E_k\).
Assuming air resistance is negligible, what is the angle of projection \(\theta\)?

Which of the following statements correctly describes the effects of air resistance on the trajectory of a projectile compared to its motion in a vacuum?

An arrow is fired with an initial speed of \(28\text{ m s}^{-1}\) at an angle of \(30^\circ\) above the horizontal over level ground.
Neglecting air resistance, what is the horizontal range of the arrow? (Take \(g = 9.81\text{ m s}^{-2}\))

A ball is projected horizontally at a speed of \(15\text{ m s}^{-1}\) from the top of a cliff. State the horizontal component of the ball's velocity after \(2.0\text{ s}\), assuming air resistance is negligible.

Explain why the horizontal and vertical motions of a projectile in a uniform gravitational field can be treated independently when air resistance is negligible.

A projectile is fired with an initial speed of \(35.0\text{ m s}^{-1}\) at an angle of \(40.0^\circ\) above the horizontal. Taking \(g = 9.81\text{ m s}^{-2}\), determine the angle the velocity vector makes with the horizontal at \(t = 3.00\text{ s}\).

A tennis ball is hit horizontally from a height of \(2.40\text{ m}\) above the ground. It lands on the ground a horizontal distance of \(15.0\text{ m}\) away. Air resistance is negligible. Take \(g = 9.81\text{ m s}^{-2}\).

(a) Calculate the time of flight of the ball.
(b) Calculate the initial horizontal velocity with which the ball was hit.
(c) Calculate the vertical component of the velocity of the ball just before it hits the ground.

An arrow is fired from ground level on flat terrain with an initial speed of \(35.0\text{ m s}^{-1}\) at an angle of \(38.0^\circ\) above the horizontal. Assume air resistance is negligible. Take \(g = 9.81\text{ m s}^{-2}\).

(a) Calculate the initial horizontal and vertical components of the velocity of the arrow.
(b) Determine the maximum height reached by the arrow above the ground.
(c) Calculate the total time the arrow is in the air before hitting the ground.
(d) Calculate the horizontal range of the arrow.