Aria J.

# Help with this long response physics problem

Students conduct an experiment to study the motion of two toy rockets. In the first experiment, rocket  X of mass  mR is launched vertically upward with an initial speed  v0 at time t=0. The rocket continues upward until it reaches its maximum height at time  t1. As the rocket travels upward, frictional forces are considered to be negligible. The rocket then descends vertically downward until it reaches the ground at time  t2. The figure above shows the toy rocket at different times of its flight. In a second experiment, which has not yet been conducted by the students, rocket  Y of mass  MR, where  MR>mR, will be launched vertically upward with an initial speed  v0 at time  t=0 until it reaches its maximum height. Rocket  Y will then descend vertically downward until it reaches the ground.Two students in the group make predictions about the motion of rocket  Y compared to that of rocket  X. Their arguments are as follows.

Student 1: “Rocket  Y will have a smaller maximum vertical displacement than rocket  X, although it is launched upward with the same speed as rocket  X and has more kinetic energy than rocket  X. Because rocket  Y will have a smaller maximum vertical displacement than rocket  X, I predict that it will take less time for rocket  Y to reach the ground compared with rocket  X.”

Student 2: “Rocket  Y will have the same maximum vertical displacement as rocket  X because both rockets have the same kinetic energy. Since both rockets will have the same maximum vertical displacement, I predict that it will take both rockets the same amount of time to reach the ground.”

(b) Use quantitative reasoning, including equations as needed, to derive expressions for the maximum heights achieved by rocket  X and rocket  Y. Express your answer in terms of  v0,  mR,  MR,  g, and/or other fundamental constants as appropriate.

Use quantitative reasoning, including equations as needed, to derive expressions for the time it takes rocket  Xand rocket  Y to reach the ground after reaching their respective maximum heights,  HX and  HY. Express your answer in terms of  v0,  mR,  MR,  HX,  HY,  g, and/or other fundamental constants as appropriate.

Heidi T.

Since these are "rockets" does the picture indicate that the rockets are propelled upward after the initial launch or are they shot upward with an initial velocity then projectile motion / freefall after?
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04/28/20

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Aria J.

thank you!
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04/30/20

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