(c) From ygt=−122, we see that the ball has reached the height of ()2212|9.80 m/s0.205 s|0.205 m−=at the moment the ball is halfway to the batter. (d) The ball’s height when it reaches the batter is 22129.80 m/s0.409 s0.820m−,which, when subtracted from the previous result, implies it has fallen another 0.615 m. Since the value of yis not simply proportional to t, we do not expect equal time-intervals to correspond to equal height-changes; in a physical sense, this is due to the fact that the initialy-velocity for the first half of the motion is not the same as the “initial” y-velocity for the second half of the motion. 40. We adopt the positive direction choices used in the textbook so that equations such as Eq. 4-22 are directly applicable. The initial velocity is horizontal so that
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