EXAMPLE 4-9 A ROUGH SHOT Chipping from the rough, a golfer sends the ball over a 3.00-m-high tree that is 14.0m away. The ball lands at the same level from which it was struck after traveling a horizontal distance of 17.8 m-on the green, of course. The ball leaves the club at 54.0" above the horizontal and lands on the green 2.24 s later. (a) What was the Initial speed of the ball? (b) How high was the ball when it passed directly over the tree? PICTURE THE PROBLEM Our sketch shows the ball taking flight from the origin, So = 19 - 0, with a launch angle of 54.0', and arcing over the tree. The individual points along the parabolic trajectory corre- 5 spond to equal time intervals. Height, y (m) REASONING AND STRATEGY a. The projectile moves with constant speed in the & direction, and hence the x component of velocity is simply the horizon- tal distance divided by time. Knowing e, and e, we can find to from e, = to coso. b. We can use x = (6, cose)t to find the time when the ball is at AS4.0 * = 14.0 m. Substituting this time into y - (to sino)f - agr 12 16 gives the height. Distance, x (m) Known Horizontal distance, d = 17.8 m; launch angle, # = 54.0,, time of flight, t - 2.24 s. Unknown (a) Initial speed, 6, = ? (b) Height of ball at tree, y = ? CONTINUEDQuestion 26 (1 point) Retake question Please refer to Example 4-9 (page 100) in the textbook. At what height, in meters, with respect to the launching point is the golf ball at time t = 1.60 s? Notice how in step 4 the appropriate kinematic equation is used. Simply plug in the value for time in the respective equation