(a) Explanation Given Information: The initial velocity ( v 0 ) of the model rocket is 75 m/s . The rocket’s land at a distance ( d ) is 100 m (from point A). The acceleration due to gravity ( g ) value is 9.81 m/s . The angle ( θ ) is 30 ° . Calculation: 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 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 Write the position ( x ) equation for horizontal motion: x = ( v 0 ) x t + 1 2 a x t 2 Substitute v 0 cos α for ( v x ) 0 and 0 for a x . x = v 0 t sin α + 1 2 a x t 2 x = v 0 t sin α + 1 2 ( 0 ) t 2 x = v 0 t sin α + 0 sin α = x v 0 t (1) Write the position ( y ) equation for vertical motion: y = ( v y ) 0 t + 1 2 a y t 2 Substitute v 0 sin α for ( v y ) 0 and –g for a y . y = v 0 t cos α + 1 2 ( − g ) t 2 y = v 0 t cos α − 1 2 g t 2 cos α = 1 v 0 t ( y + 1 2 g t 2 ) (2) Find the expression to calculate the time (t) using the formula. sin 2 α + cos 2 α = 1 Substitute x v 0 t for sin α and 1 v 0 t ( y + 1 2 g t 2 ) for cos α . ( x v 0 t ) 2 + ( 1 v 0 t ( y + 1 2 g t 2 ) ) 2 = 1 1 ( v 0 t ) 2 ( x 2 + ( y + 1 2 g t 2 ) 2 ) = 1 x 2 + y 2 + g y t 2 + 1 4 g 2 t 4 = ( v 0 t ) 2 x 2 + y 2 + g y t 2 + 1 4 g 2 t 4 − v 0 2 t 2 = 0 1 4 g 2 t 4 − ( v 0 2 − g y ) t 2 + ( x 2 + y 2 ) = 0 (3) Write the coordinates ( x ) : x = d cos ( θ ) Substitute 30 ° for θ and 100 m for d (b) To determine The maximum height ( y max ) above point A reached by the rocket. (c) To determine The time ( t ) duration of the flight.

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Author: BEER

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Chapter 11.4, Problem 11.112P

(a)

To determine

The angle (α) that (v0) forms with the vertical.

(b)

To determine

The maximum height (ymax) above point A reached by the rocket.

(c)

To determine

The time (t) duration of the flight.

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Chapter 11.4, Problem 11.111P

Chapter 11.4, Problem 11.113P

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The angle ( α ) that ( v 0 ) forms with the vertical.

Solution Summary: The author calculates the x component initial velocity (v_0), the acceleration due to gravity (g) value is 9.81m/s and the

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The angle (α) that (v0) forms with the vertical.

The maximum height (ymax) above point A reached by the rocket.

The time (t) duration of the flight.

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Chapter 11 Solutions