(6%) Problem 6: During a baseball game, a baseball is struck at ground level by a batter. The ball leaves the baseball bat with an initial speed vo = 48 m/s at an angle 6 = 28 above horizontal. Let the origin of the Cartesian coordinate system be the ball's position the instant it leaves the bat. Air resistance may be ignored throughout this problem. 20% Part (a) Express the magnitude of the ball's initial horizontal velocity Vo, in terms of vo and e. VO

20% Part (1) Express the magnitude of the ball's initial vertical velocity vo, in terms of vo and e. 20% Part (c) Find the ball's maximum vertical height hmar in meters above the ground. 20% Part (d) Enter an expression in terms of vo, 0, and g for the time Imax it takes the ball to travel to its maximum vertical height. 20% Part (e) Calculate the horizontal distance xmax in meters that the ball has traveled when it returns to ground level.

## Answer

@ horizontal velouity component [x = Vo cose ] 6 Vo = 48 wils. vertical velocity component. Į voy = vo fino - - - Vaino 40=261 ولاد - 0 initial vestical velocity voy = voisine final vestical velocity (velocity at maximum night) =O = (vorg) ² - 2.9x hmax huaax = (Vas)? - von since Therapa upe. (sin28) = 169 m) taken to reach maximum hight. 0= (voy) - gxt 2x9.8 time horizontal dig dance amax = vo since ug². sinst = 194.9 m. 9.8

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