(a) Explanation Given Information: The initial velocity ( v 0 ) of the ball is 108 km/h at an angle ( α ) . The difference in height ( y ) of the ball at position A and B is 0.08 m . The horizontal distance between the A and B is 14 m . The acceleration due to gravity ( g ) value is 9.81 m/s 2 . Calculation: Convert kilometer per hour to meter per second. v 0 = 108 km / h × 1 000 m 1 km × 1 hr 3600 sec = 30 m/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 30 km/h for v 0 . ( v x ) 0 = 30 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 30 km/h for v 0 . ( v y ) 0 = 30 sin α Calculate the x component acceleration ( a y ) using the relation: a y = − g Write the position equation ( x ) for horizontal motion: x = x 0 + ( v 0 ) x t + 1 2 a x t 2 Here, x 0 is initial position of the ball in horizontal direction. Substitute 14 m for x , 30 cos α for ( v 0 ) x , 0 for x 0 , and 0 for a x (b) To determine The angle ( θ ) that the velocity of the ball at point B forms with the horizontal.

Vector Mechanics for Engineers: Statics and Dynamics

12th Edition

ISBN: 9781259977251

Author: BEER

Publisher: MCG

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Chapter 11.4, Problem 11.111P

(a)

To determine

The angle (α).

(b)

To determine

The angle (θ) that the velocity of the ball at point B forms with the horizontal.

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Chapter 11.4, Problem 11.110P

Chapter 11.4, Problem 11.112P

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The angle ( α ) .

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