(a) Explanation Given Information: The initial velocity ( v 0 ) of the hockey puck is 90 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 = 90 mi/h × 5280 ft 1 mi × 1 hr 3600 sec = 132 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 132 ft/s for v 0 . ( v x ) 0 = 132 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 132 ft/s for v 0 . ( v y ) 0 = 132 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 , 132 cos α for ( v x ) 0 and 0 for a x . x = 0 + 132 cos α t + 1 2 ( 0 ) t 2 = 132 cos α t Modify the above equation for time ( t ). Substitute 16 ft for x . 16 = 132 cos α t t enter = 16 132 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 , 132 sin α for ( v y ) 0 , and –g for a y . y = 0 + 132 sin α t + 1 2 ( − g ) t 2 = 132 sin α t − 1 2 g t 2 Substitute t enter for t . y = 132 sin α t enter − 1 2 g t enter 2 (2) Substitute Equation (1) in Equation (2). y = 132 sin α ( 16 132 cos α ) − 1 2 g ( 16 132 cos α ) 2 = 16 tan α − 32 g 4356 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.

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ISBN: 9781260265453

Author: BEER

Publisher: MCG

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

Solution Summary: The author calculates the x component initial velocity (v_0) using the relation.