To determine (a) The equation of rocket’s trajectory (b) Shape of trajectory (c) Elevation of rocket Explanation Part (a): Velocity is basically a speed of a particle in a particular direction with magnitude. It is the ratio of the displacement per unit time. It is expressed by the expression as given below: v = x t …… (1) Here, x is displacement traveled by the body in time t . The SI unit of velocity is meter per second m/s . So, the motion of rocket in horizontal x-direction is given by using equation (1) below: x = v x t v x = v cos θ = a x t …… (2) Here, θ is the angle formed with horizontal component. By using Newton’s equation of motion, the motion of rocket in vertical y-direction is given below: s = v t + 1 2 a t 2 y = v sin θ t − 1 2 a t 2 …… (3) Part (c): Total force F y in the y-direction is force of thrust in upward so F = F thrust sin θ and normal force in downward direction so F N = m g F y = m a y a y = F y m a y = F sin θ − m g m …… (4) Here, u is the initial velocity of the rocket, v is the final velocity of the rocket, and s is the distance covered the rocket. Initial velocity of the rocket in both the x- and y-direction is zero. So the expression for final velocity of the rocket to reach the speed of the sound is given as follows: v y 2 = 2 a y y y = v y 2 2 a y ……. (5) Given: Mass of interceptor rocket m = 5000 kg Thrust of rocket F thrust = 140700 N Speed of sound v = 330 m/s Rocket launched at angle θ = 44.7 ο Formula used: v = x t y = v sin θ t − 1 2 a t 2 F = m a Calculation: Part (a): Substitute, equation (2) in equation (3), so the equation in terms of y as a function of x that shows the rocket’s trajectory is given as follows: y ( x ) = v sin θ ( x v cos θ ) − 1 2 g ( x v x ) 2 y ( x ) = x tan θ − 1 2 g ( x v x ) 2 …… (6) Part (b): Equation (6) shows the equation of parabola and its axis is parallel to y-axis

Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (Chs 1-42) Plus Mastering Physics with Pearson eText -- Access Card Package (4th Edition)

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Chapter 8, Problem 34EAP

To determine

(a) The equation of rocket’s trajectory

(b) Shape of trajectory

(c) Elevation of rocket

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Chapter 8, Problem 33EAP

Chapter 8, Problem 35EAP

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (Chs 1-42) Plus Mastering Physics with Pearson eText -- Access Card Package (4th Edition)

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