Explanation Given: The acceleration a y is ( − 9.81 m/s 2 ) . The dart’s velocity υ A is 10 m/s . The angle at C is θ C . The angle at D is θ D . The distance ( s B ) x is 5 m . The distance and angle is shown in Figure (1). Write the expression for final distance in x direction. ( s B ) x = ( s A ) x + ( υ A ) x t (I). Here, final distance in the horizontal direction is ( s B ) x , initial distance in the horizontal direction is ( s A ) x , initial velocity in the horizontal direction is ( υ A ) x and time is t . Write the expression for final velocity in y direction. ( υ B ) y = ( υ A ) y + a y t (II). Here, final velocity in the vertical direction is ( υ B ) y , initial velocity in the vertical direction is ( υ A ) y , acceleration due to gravity is a y and time is t . Write the expression for difference in time. △ t = t C − t D (III). From Figure (1) write the expression for ( υ A ) x . ( υ A ) x = υ A cos θ (IV). From Figure (1) write the expression for ( υ A ) y . ( υ A ) y = υ A sin θ (V). Conclusion: Substitute 10 m/s for υ A in Equation (IV). ( υ A ) x = υ A cos θ = 10 cos θ Substitute 10 m/s for υ A in Equation (V). ( υ A ) y = υ A sin θ = 10 sin θ From Figure (1) substitute 5 m for ( s B ) y , 0 for ( s A ) x and 10 cos θ for ( υ A ) x in Equation (I). ( s B ) x = ( s A ) x + ( υ A ) x t 5 = 0 + 10 cos θ t t = 5 10 cos θ (VI) Substitute − 10 sin θ for ( υ ) y , 10 sin θ for ( υ A ) y , − 9

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Chapter 12, Problem 104P

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The angles θC and θD at which darts should be thrown and the time between each throw.

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The angles θ C and θ D at which darts should be thrown and the time between each throw.

Solution Summary: The distance and angle is shown in Figure (1). Write the expression for final distance in x direction.

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The angles θC and θD at which darts should be thrown and the time between each throw.

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