Catapulted A stone is catapulted rightward with aninitial velocity of 29.0 m/s a

Question

Catapulted A stone is catapulted rightward with aninitial velocity of 29.0 m/s at anangle of 41.0° above level ground.Neglect air resistance. Find its horizontal and verticaldisplacements at the following times after launch. (a) 0.90 s
1???m (horizontal)
2?? m (vertical)
(b) 1.80 s
?? ??m (horizontal)
4?? m (vertical)
(c) 3.88 s
5??? m (horizontal)
6??? m (vertical) (a) 0.90 s
1???m (horizontal)
2?? m (vertical)
(b) 1.80 s
?? ??m (horizontal)
4?? m (vertical)
(c) 3.88 s
5??? m (horizontal)
6??? m (vertical)

Explanation / Answer

   Let U = initial velocity = 29.0 m/s           = angle of projection = 41.0°       Initial velocity in horizontaldirection , Ux = U cos = 21.87 m/s       Vertical component of initialvelocity, Uy = U sin = 19.03 m/s         Horizontaldisplacement , X = ( Ux ) t         Verticaldisplacement , Y = ( Uy) t - (1/2) g t2 (a)   t = 0.9 s        Horizontaldisplacement , X = ( 21.87 ) * ( 0.9 ) = 19.68m      Vertical displacement , Y = ( 19.03 )* ( 0.9 ) - (1/2) * ( 9.8 ) * ( 0.9) 2 =17.13 - 3.97 = 13.16 m (b)   t = 1.8 s        Horizontaldisplacement , X = ( 21.87 ) * ( 1.8 ) = 39.37m      Vertical displacement , Y = ( 19.03 )* (1.8 ) - (1/2) * ( 9.8 ) * ( 1.8) 2 =34.25- 15.88 = 18.37 m (c)   t = 3.88 s        Horizontaldisplacement , X = ( 21.87 ) * ( 3.88 ) =84.86 m      Vertical displacement , Y = ( 19.03 )* ( 3.88 ) - (1/2) * ( 9.8 ) * ( 3.88 )2 = 73.84 - 73.77= 0.07 m (a)   t = 0.9 s        Horizontaldisplacement , X = ( 21.87 ) * ( 0.9 ) = 19.68m      Vertical displacement , Y = ( 19.03 )* ( 0.9 ) - (1/2) * ( 9.8 ) * ( 0.9) 2 =17.13 - 3.97 = 13.16 m (b)   t = 1.8 s        Horizontaldisplacement , X = ( 21.87 ) * ( 1.8 ) = 39.37m      Vertical displacement , Y = ( 19.03 )* (1.8 ) - (1/2) * ( 9.8 ) * ( 1.8) 2 =34.25- 15.88 = 18.37 m (c)   t = 3.88 s        Horizontaldisplacement , X = ( 21.87 ) * ( 3.88 ) =84.86 m      Vertical displacement , Y = ( 19.03 )* ( 3.88 ) - (1/2) * ( 9.8 ) * ( 3.88 )2 = 73.84 - 73.77= 0.07 m        Horizontaldisplacement , X = ( 21.87 ) * ( 1.8 ) = 39.37m      Vertical displacement , Y = ( 19.03 )* (1.8 ) - (1/2) * ( 9.8 ) * ( 1.8) 2 =34.25- 15.88 = 18.37 m (c)   t = 3.88 s        Horizontaldisplacement , X = ( 21.87 ) * ( 3.88 ) =84.86 m      Vertical displacement , Y = ( 19.03 )* ( 3.88 ) - (1/2) * ( 9.8 ) * ( 3.88 )2 = 73.84 - 73.77= 0.07 m        Horizontaldisplacement , X = ( 21.87 ) * ( 3.88 ) =84.86 m      Vertical displacement , Y = ( 19.03 )* ( 3.88 ) - (1/2) * ( 9.8 ) * ( 3.88 )2 = 73.84 - 73.77= 0.07 m

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