Question

A rocket is initially at rest on the launch pad. the engine fires and the rocket accelerates vertically at 20 m/s^2 for 60 seconds. Afterwards, the engine shuts off. What is the altitude and velocity of the rocket when the engine shuts off? What is the maximum height reached?

Answer 1

The altitude and velocity of the rocket when the engine shuts off are 36000 m and 1200 m/s, respectively. The maximum height reached by the rocket is 7346.94 m.

Step-by-step explanation:

To find the altitude and velocity of the rocket when the engine shuts off, we can use the equations of motion. The rocket accelerates at 20 m/s² for 60 seconds, so the final velocity would be 20 m/s² * 60 seconds = 1200 m/s. The average velocity during this time would be (0 m/s + 1200 m/s) / 2 = 600 m/s. Assuming the rocket was initially at rest, the altitude can be found using the equation: altitude = (average velocity) * time = 600 m/s * 60 seconds = 36000 m.

The maximum height reached can be found using the equation: maximum height = (initial velocity)² / (2 * acceleration). Since the engine shuts off after 60 seconds, the initial velocity would be 20 m/s² * 60 seconds = 1200 m/s. So, the maximum height would be (1200 m/s)² / (2 * (-9.8 m/s²)) = 7346.94 m.