A small rocket is fired from a launch pad 15 m above the ground with an...

 

Transcribed Image Text:

A small rocket is fired from a launch pad 15 m above the ground with an initial velocity (300,400,450) m/s. A cross wind blowing to the north produces an acceleration of the rocket of 3 m/s. ASsume the x-axis points east, the y-axis points north, the positive z-axis is vertical (opposite g), and the ground is horizontal. Answer parts a through d. a. Find the velocity and position vectors for t2 0. The velocity vector is v(t) = a. Find the velocity and position vectors for t20. Recall that the velocity is the antiderivative of the acceleration. Determine the acceleration vector. Note that the accelerations acting on the rocket are gravity in the vertical direction and wind blowing to the north. Note that the gravity is g=9.8 m/s2. b. Make a sketch of the trajectory. Plot the position vector to find the trajectory. The correct graph is shown to the right. c. Determine the time of flight and range of the object. Notice that the rocket hits the ground when the z-component of the position vector, or the height of the rocket, is equal to zero. d. Determine the maximum height of the object. Notice that when the vertical velocity of the rocket is equal to zero, the rocket is at its highest point. A small rocket is fired from a launch pad 15 m above the ground with an initial velocity (300,400,450) m/s. A cross wind blowing to the north produces an acceleration of the rocket of 3 m/s. ASsume the x-axis points east, the y-axis points north, the positive z-axis is vertical (opposite g), and the ground is horizontal. Answer parts a through d. a. Find the velocity and position vectors for t2 0. The velocity vector is v(t) = a. Find the velocity and position vectors for t20. Recall that the velocity is the antiderivative of the acceleration. Determine the acceleration vector. Note that the accelerations acting on the rocket are gravity in the vertical direction and wind blowing to the north. Note that the gravity is g=9.8 m/s2. b. Make a sketch of the trajectory. Plot the position vector to find the trajectory. The correct graph is shown to the right. c. Determine the time of flight and range of the object. Notice that the rocket hits the ground when the z-component of the position vector, or the height of the rocket, is equal to zero. d. Determine the maximum height of the object. Notice that when the vertical velocity of the rocket is equal to zero, the rocket is at its highest point.