(a) Explanation Given Information: The initial velocity ( v 0 ) of the hockey puck is 105 mi/h . The distance ( x ) between point A to B is 16 ft . The acceleration due to gravity ( g ) value is 32.2 ft/s 2 . The height of the net ( y front ) is 4 ft . Calculation: Convert mile per hour to feet per second. v 0 = 105 mi/h × 5280 ft 1 mi × 1 hr 3600 sec = 154 ft/s Write the coordinate for point A : ( x 0 , y 0 ) = ( 0 , 0 ) Calculate the x component initial velocity ( v x ) 0 using the relation: ( v x ) 0 = v 0 cos α Substitute 154 ft/s for v 0 . ( v x ) 0 = 154 cos α Calculate the x component acceleration ( a x ) using the relation: a x = 0 Calculate the y component initial velocity ( v y ) 0 using the relation: ( v y ) 0 = v 0 sin α Substitute 154 ft/s for v 0 . ( v y ) 0 = 154 sin α Calculate the y component acceleration ( a y ) using the relation: a y = − g Write the position ( x ) equation for horizontal motion: x = x 0 + ( v x ) 0 t + 1 2 a x t 2 Here, x 0 is initial position of hockey puck in x axis. Substitute0 for x 0 , 154 cos α for ( v x ) 0 , and 0 for a x . x = 0 + 154 cos α t + 1 2 ( 0 ) t 2 = 154 cos α t Modify the above equation for time ( t ). Substitute 16 ft for x . 16 = 154 cos α t t enter = 16 154 cos α (1) Write the position ( y ) equation for vertical motion: y = y 0 + ( v y ) 0 t + 1 2 a y t 2 Here, y 0 is initial position of hockey puck in y axis. Substitute 0 for y 0 , 154 sin α for ( v y ) 0 , and –g for a y . y = 0 + 132 sin α t + 1 2 ( − g ) t 2 = 154 sin α t − 1 2 g t 2 Substitute t enter for t . y = 154 sin α t enter − 1 2 g t enter 2 (2) Substitute Equation (1) in Equation (2). y = 154 sin α ( 16 154 cos α ) − 1 2 g ( 16 154 cos α ) 2 = 16 tan α − 128 g 23716 cos 2 α (3) Since 1 cos 2 α = sec 2 α = 1 + tan 2 α (b) To determine The time ( t enter ) required for the puck to reach the net.

Vector Mechanics for Engineers: Statics and Dynamics

11th Edition

ISBN: 9780073398242

Author: Ferdinand P. Beer, E. Russell Johnston Jr., David Mazurek, Phillip J. Cornwell, Brian Self

Publisher: McGraw-Hill Education

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Chapter 11.4, Problem 11.113P

(a)

To determine

The largest value of angle (αmax) for which the puck will enter the net.

(b)

To determine

The time (tenter) required for the puck to reach the net.

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Chapter 11.4, Problem 11.112P

Chapter 11.4, Problem 11.114P

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Vector Mechanics for Engineers: Statics and Dynamics

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The largest value of angle ( α max ) for which the puck will enter the net.