4.2 横向发射物体的投射动作

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• 选择节横向发射物体的投射动作

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  横向发射物体的投射动作

  

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  The activity of bike jumping, like other sports that involve vector motions in perpendicular directions, requires more physical practice than mathematical analysis.  The laws of physics apply to the activity, however, whether the biker is aware of them or not.
  ::自行车跳跃活动与其他运动一样,涉及直角方向的矢量运动,需要比数学分析更多的物理实践。 但是,物理学法则适用于活动,无论自行车手是否意识到它们。

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  Projectile Motion for an Object Launched Horizontally
  ::横向发射物体的投射动作

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  Objects that are launched into the air are called projectiles . The path followed by a projectile in motion is called a trajectory . The image of the snowboarder in the chapter introduction showed his trajectory; every object has a trajectory even when we cannot see it. , or the object's trajectory, is described in terms of position, , and . Even with only an object's current location, velocity, and acceleration, we can calculate when and where the object will land. Our knowledge that perpendicular components of do not affect each other allow us to easily analyze the motion of projectiles.
  ::射入空气的物体称为射弹。 弹丸运动所沿循的路径被称为轨迹。 章导言中滑雪机的图像显示了他的轨迹; 每一个物体都有轨迹, 即使我们看不到它。 或物体的轨迹, 都用位置来描述, 并且 。 即使只有物体目前的位置、 速度和加速度, 我们也可以计算物体降落的时间和地点。 我们知道物体的垂直组成部分不会相互影响, 使我们很容易地分析射弹的动向 。

  

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  In the diagram, two balls (one red and one blue) are dropped at the same time.  The red ball is released with no horizontal motion and the blue ball is dropped but also given a horizontal velocity of 10 m/s.  As the balls fall to the floor, a photograph is taken every second so that in 5 seconds, we have 5 images of the two balls.  Each vertical line on the diagram represents 5 m. Since the blue ball has a horizontal velocity of 10 m/s, you will see that for every second, the blue ball has moved horizontally 10 m.  That is, in each second, the blue ball has increased its horizontal by 10 m. This horizontal motion is due to the ball's constant velocity.
  ::在图表中,两个球(一个红色球和一个蓝色球)同时投下。红色球在无水平运动的情况下释放出来,蓝色球在无水平运动的情况下被投下,但水平速度为10米/秒。球落在地上时,每秒拍一张照片,这样5秒内,我们就有5个两个球的图像。图上的每条垂直线代表5米。由于蓝色球水平速度为10米/秒,每秒,蓝色球水平移动10米。即每秒,蓝色球水平上升10米。这一水平运动是由于球的恒定速度造成的。

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  The red ball was dropped straight down with no horizontal velocity and therefore, in each succeeding second, the red ball falls straight down with no horizontal motion. The increasing distances between seconds in the red ball's motion indicates that this motion is accelerating.
  ::红色球直直投下来,没有水平速度,因此,在接下来的每秒,红色球直投下来,没有水平运动。红球运动中各秒之间的距离越来越大,这表明这一动作正在加速。

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  A very important point here is that the vertical motion of these two balls is identical.  That is, they each fall exactly the same distance vertically in each succeeding second. The constant horizontal velocity of the blue ball has no effect on its accelerated vertical motion. Therefore, the vertical motion of the blue ball can be analyzed exactly the same as the vertical motion of the red ball.
  ::这里一个非常重要的一点是,这两个球的垂直运动是相同的。 也就是说, 每个球的垂直运动都是相同的。 每个球的垂直速度都是相同的。 蓝色球的不变水平速度对其加速的垂直运动没有影响。 因此, 蓝色球的垂直运动可以和红色球的垂直运动完全一样地分析。

   

   

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  Examples
  ::实例

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  Example 1 
  ::例1

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  If an arrow is fired from a bow with a perfectly horizontal velocity of 60.0 m/s and the arrow was 2.00 m above the ground when the it was released, how far will the arrow fly horizontally before it strikes the ground?
  ::如果箭是从弓上射出的,其水平速度完全为60.0米/秒,而箭在释放时在地面上方为2.00米,箭在射入地面前水平飞到多远?

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  This problem is solved by determining how long it takes the arrow to fall to the ground in exactly the same manner as if the arrow was dropped with no horizontal velocity. The time required for the arrow to fall to the ground will be the same time that the arrow flies horizontally at 60.0 m/s, so
  ::通过确定箭头以与箭头无水平速度投下完全相同的方式坠落到地上需要多久才能解决这个问题。箭头坠落到地上所需要的时间与箭头水平在60.0m/s水平飞行的时间相同,因此,

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  $\begin{array}{r}d=\frac{1}{2}a{t}^2\text{solved for}t=\sqrt{\frac{2d}{a}}=\sqrt{\frac{(2)(2.00\text{m})}{9.80{\text{m/s}}^2}}=0.639\text{s}\end{array}$
  ::t=2da=(2)2.00米)9.80米/秒=0.639秒 d=12at2溶解

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  The time required for the fall is multiplied by the horizontal velocity to get the horizontal distance.
  ::下降所需的时间乘以水平速度以获得水平距离。

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  $\begin{array}{r}{d}_{\text{horizontal}}=(v_{\text{horizontal}})(\text{time})=(60.0\text{m/s})(0.639\text{s})=38.3\text{m}\end{array}$
  ::dorizontal=( vholizontal( 时间) =( 60.0 m/ s)( 0. 639 s) = 38.3 m

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  Example 2  
  ::例2

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  A rock was thrown horizontally from a 100.0 m high cliff. It strikes the ground 90.0 m from the base of the cliff. At what was it thrown?
  ::从100.0米高的悬崖水平向上投掷了一块岩石,从悬崖底部向地表90.0米处撞击。

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  We can calculate how long it takes for a rock to free fall 100.0 m and then divide this time into the horizontal distance to get the horizontal velocity.
  ::我们可以计算一个岩石要多久才能自由掉下来 100.0米 然后将这个时间分成水平距离 才能达到水平速度

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  $$\begin{array}{rl}t& =\sqrt{\frac{2d}{a}}=\sqrt{\frac{(2)(100.0\text{m})}{9.80{\text{m/s}}^2}}=4.52\text{s}\\ v& =\frac{d}{t}=\frac{90.0\text{m}}{4.52\text{s}}=19.9\text{m/s}\end{array}$$

  
  ::t=2da=(2)(2)-10.0m)9.80米/s2=4.52sv=dt=90.0m4.52s=19.9m/s

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  Use the following simulation to adjust the initial velocity and height of a launched arrow and try to predict whether or not the archer will hit her target:
  ::使用以下模拟来调整发射箭头的初始速度和高度,并试图预测箭头是否击中目标:

   

   

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  Further Reading
  ::继续阅读

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  Summary
  ::摘要

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  • Perpendicular components of vectors do not influence each other.
    ::病媒的垂直成份互不影响。
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  • The horizontal motion of a projectile does not influence its free fall.
    ::弹丸的横向运动并不影响其自由坠落。

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  Review
  ::回顾

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  1. If a tennis ball is thrown horizontally at the exact time a duplicate tennis ball is dropped by hand at the same height, which ball will hit the ground first?
     
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     1. the one dropped straight down
        ::直直下降的一滴
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     2. the one fired horizontally
        ::一个横向发射
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     3. both will hit the ground at the same time
        ::两者同时撞击地面
     
     ::如果一个网球在同一个高度用手投下一个重复的网球时被水平投向同一高度,哪个球先打到地面?一个球直接投向一个横向发射的球,两个球同时打到地面。
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  2. A cannon is fired from the edge of a small cliff.  The height of the cliff is 80.0 m.  The cannon ball is fired with a perfectly horizontal velocity of 80.0 m/s.  How far will the cannon ball fly horizontally before it strikes the ground?
     ::大炮从小悬崖边缘发射,悬崖高度为80.0米。大炮的发射速度是完全水平的80.0米/秒。大炮炮弹在撞击地面之前水平飞到多远?
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  3. A cliff diver running 3.60 m/s dives out horizontally from the edge of a vertical cliff and reaches the water below 2.00 s later.  How high is the cliff and how far from the base of the cliff did the diver hit the water?
     ::悬崖潜水员从垂直悬崖边缘水平下潜3.60米/秒,然后到达2.00秒以下的水面。悬崖有多高,潜水员在离悬崖底部多远时击中了水面?