4-47. The “Vomit Comet.” In zero

4-47. The “Vomit Comet.” In zero-gravity astronaut training and equipment testing, NASA flies a
KC135A aircraft along a parabolic flight path. As shown in Figure P4.47, the aircraft climbs from
24 000 ft to 31 000 ft, where it enters the zero-g parabola with a velocity of 143 m/s nose high at
45.0° and exits with velocity 143 m/s at 45.0° nose low. During this portion of the flight, the aircraft
and objects inside its padded cabin are in free fall; they have gone ballistic. The aircraft then pulls
out of the dive with an upward acceleration of 0.800g, moving in a vertical circle with radius 4.13
km. (During this portion of the flight, occupants of the aircraft perceive an acceleration of 1.8g.)
What are the aircraft’s (a) speed and (b) altitude at the top of the maneuver? (c) What is the time
interval spent in zero gravity? (d) What is the speed of the aircraft at the bottom of the flight path?
[Ans] [註] 這是真實的太空人無重力訓練方式。 4-50. A basketball player who is 2.00 m tall is standing on the floor 10.0 m from the basket. If he
shoots the ball at a 40.0o angle with the horizontal, at what initial speed must he throw so that it goes
through the hoop without striking the backboard? The basket height is 3.05 m. [Ans] x f  vix t  vi t cos 40.0
Thus, when x f  10.0 m , t 
10.0 m
.
vi cos 40.0
At this time, y f should be 3.05 m  2.00 m  1.05 m .
Thus,
 v sin 40.0 10.0 m  1
1.05 m  i
vi cos 40.0
2
 9.80 m s 
2
2
 10.0 m 

 .
 vi cos 40.0 
From this, vi  10.7 m s .
[註] 三分球線距籃框 6.24 – 7.24 m，所以這個球員站太遠投籃了。 vi 是球的初速，球員在不同
的位置投籃，必須先以上述式子算出 vi ，決定了出手力道，才能把球投進。但這顯然是不可能
的，大部分球員根本不會算拋體運動，他們只是根據練習了千百次的經驗把球投出去，就是
靠”手感”。物理和籃球的關係後面的章節還會再提到。
4-58. When baseball players throw the ball in from the outfield, they usually allow it to take one
bounce before it reaches the infield on the theory that the ball arrives sooner that way. Suppose the
angle at which a bounced ball leaves the ground is the same as the angle at which the outfielder
threw it as shown in Figure P4.58, but the ball’s speed after the bounce is one-half of what it was
before the bounce. (a) Assume the ball is always thrown with the same initial speed. At what angle u
should the fielder throw the ball to make it go the same distance D with one bounce (blue path) as a
ball thrown upward at 45.0° with no bounce (green path)? (b) Determine the ratio of the time
interval for the one-bounce throw to the flight time for the no-bounce throw.
[Ans] [註] 跳兩次比跳一次快到! 當然這和棒球場地面的彈性有關。