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# How far from the bottom of the chute does the ball land? your answer for the distance the ball travels from the end of the chute should contain r? Mindee Nelson

in Physics

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#### 1 answer Amanda Johnson on February 14, 2019

To get the distance, find the unchanging horizontal component of the velocity and the time-of-flight and multiply them.In the first place, find the horizontal component of the speed Vh by using the equation for centripetal acceleration: v2 / r = a Vh2 / R = 2g V = 2g therefore, the horizontal component of the velocity is: ►Vh = √( 2gr ) Now to find the elapsed time. In the vertical dimension, the ball began its flight without initial velocity. We can determine how far it moves vertically by the equation: d = ½at2 And substitute our values for d and a and solve for time: 2R = ½gt2 t2 = 4R / g t = √( 4R / (g ) t = 2√( R / g ) ►∆t = 2√( R / g ) Now we multiply our two critical values to obtain the distance: d = V•∆t d = [ √( 2gr ) ]•[ 2√( R / g ) ] d = 2√( 2 R2 ) d = 2√2 R