拋體運動：練習題

A projectile is launched from a horizontal surface with an initial velocity \( u \) at an angle \( \theta \) to the horizontal. Assuming air resistance is negligible, which statement correctly describes the horizontal component of the projectile's velocity during its flight?

A projectile is launched horizontally from the top of a vertical cliff of height \( h \) with an initial velocity \( u \). It hits the horizontal ground at the base of the cliff at an angle of \( 45^\circ \) to the horizontal. Air resistance is negligible. Which of the following expressions is correct?

A ball is launched from horizontal ground with an initial speed of \( 20 \, \text{m s}^{-1} \) at an angle of \( 30^\circ \) to the horizontal. Assuming air resistance is negligible and the acceleration of free fall is \( 9.81 \, \text{m s}^{-2} \), what is the maximum vertical height reached by the ball above the ground?

Two projectiles, P and Q, are launched from a horizontal surface with the same initial speed \( u \). Projectile P is launched at an angle of \( 30^\circ \) to the horizontal, and projectile Q is launched at an angle of \( 60^\circ \) to the horizontal. Air resistance is negligible. What is the ratio of the time of flight of P to the time of flight of Q?

A small ball is projected horizontally at a speed of \( 15.0 \, \text{m s}^{-1} \) from the top of a vertical wall of height \( 45.0 \, \text{m} \). Air resistance is negligible. Using \( g = 9.81 \, \text{m s}^{-2} \), what is the horizontal distance from the base of the wall to the point where the ball hits the ground?

Explain the independence of the vertical and horizontal components of a projectile's motion and state which component is affected by the acceleration of free fall \(g\).

A projectile is launched from a point at height \( H \). If air resistance is included in the model, describe how the maximum height and horizontal range reached would change compared to a model with no air resistance.

A projectile is launched from the top of a \( 25.0 \, \text{m} \) tall building at an angle of \( 30.0^\circ \) above the horizontal with an initial speed of \( 20.0 \, \text{m s}^{-1} \). Calculate the total time of flight until the projectile hits the level ground below and determine its final speed just before impact, ignoring air resistance.

A small projectile is launched from a point \( P \) which is \( 2.0 \, \text{m} \) above a horizontal landing plane. The initial velocity of the projectile is \( 25.0 \, \text{m s}^{-1} \) at an angle of \( 40.0^\circ \) above the horizontal. At a horizontal distance of \( 55.0 \, \text{m} \) from \( P \), there is a tall vertical barrier. Air resistance is negligible.

(a) Show that the horizontal component of the velocity is approximately \( 19.2 \, \text{m s}^{-1} \).
(b) Calculate the time of flight for the projectile until it strikes the barrier.
(c) Determine the height above the landing plane at which the projectile strikes the barrier.
(d) Calculate the magnitude of the velocity of the projectile at the instant it strikes the barrier.
(e) Suggest one reason why the actual height reached by a projectile in a laboratory experiment would be less than the value calculated in part (c).