Question

You are working with a group of interns at a commercial rocket company. They are testing the feasibility of launching rockets with catapults to reach the upper atmosphere, where they will release a payload of small weather balloons. You have been given the task of determining the path of a rocket under the following conditions: The catapult launches the rocket from an underground silo at 60.0° above the horizontal such that it has a speed of 100 m/s, in a direction toward the ocean, just as the tail end of the rocket arrives at ground level. At that instant, the rocket engine immediately starts a burn, which lasts for 32.0 s, during which the rocket moves along its initial line of motion with a constant acceleration of 32.0 m/s². After the burn, the fuel runs out and the rocket proceeds to move in free fall, with its tail end downward. Your supervisor has asked you to ignore air resistance and determine the maximum height of the tail end of the rocket above the ground, the total time interval during which the rocket is in the air, and where to locate a recovery team to be ready to retrieve the rocket from its landing in the ocean.

(a)

Determine the maximum height (in km) of the tail end of the rocket above the ground.

km

(b)

Determine the total time interval (in s) during which the rocket is in the air.

s

(c)

Determine where to locate a recovery team to be ready to retrieve the rocket from its landing in the ocean. (Give your answer in km downrange from the launch.)

km

Answer 1