2-Stage Rocket Problem:
A rocket accelerates upward at 15 m/s^2 for 10 seconds starting from rest. After 10 seconds, the engine cuts off. (a) What is the maximum height the rocket will achieve? (b) What is the rocket's total flight time?
How Do I Solve The 2-Stage Rocket Kinematic Problem?
(1) In order to calculate the maximum height, you need to break the problem into two parts. You need to calculate the distance traveled by the rocket while it's accelerating upward at 15 m/s^2 for the first 10 seconds. You can use the formula d = vt + 1/2at^2.
(2) Next, you need to calculate the upward velocity attained by the rocket in the first 10 seconds. You can use the formula Vf = Vo + at.
(3) Once you know the upward velocity at t = 10s, you can calculate the vertical displacement of the rocket when the engine cuts off while it's still moving upward. You can use the formula Vf^2 = Vo^2 + 2ad to solve for 'd'. Vf - the final upward velocity of the rocket will be zero when it reaches its maximum height. The acceleration 'a' will be the acceleration due to gravity which is -9.8 m/s^2.
(4) The maximum height will be the sum of the distance traveled by the rocket in parts (1) and (3).
(5) In order to calculate the total time of flight, you need to break the problem into three parts. You already have the time of flight during the 1st part when the rocket accelerates upward for 10 seconds. You need to calculate the time of flight during the second part when the rocket's engine cuts off but while it's still moving upward in part (3). Finally, you need to calculate the time it takes for the rocket to fall down from its maximum height to the ground under the influence of gravity. Taking the sum of these three time values will give you the total flight time. You can watch the video for a visual explanation.
Distance, Displacement, Average Speed, & Average Velocity:
Kinematics In One Dimension:
Introduction to Acceleration and Velocity: