Relative velocity & Quantum mechanics (I think?)

[Subrosian]

1. The problem statements, all variables and given/known data
1. A plane leaves the ground and rises at an angle of 25º. If its speed relative to the ground is 210 mph, what is its speed relative to the air?

A. 232 mph
B. 210 mph
C. 190 mph
D. 89 mph

2. What happens to water molecules when they go from a solid to a liquid?

A. They slow down as ice melts.
B. Nothing.
C. They speed up as ice melts.
D. They get really cold as ice is formed.

Homework Equations

I'm not sure if any equations are necessary for either of the questions, but maybe
v_air = v_ground - v_wind

3. The attempt at solutions
I think the answer to the first question is B, because the air has no defined velocity and thus there should be no difference in relative velocity whether it's on the ground or in the air. However, I'm not sure if the fact that it rose to the air means that a vertical component is added to the plane's velocity, which would make the resulting velocity 210mph/cos(25), equivalent to 232mph (answer A.)

As for the second question, I don't think that C is true, because water molecules do not increase in temperature, and therefore speed, during change in state. What I learned in Chemistry is that the energy used during state change is used for breaking their intermolecular bonds. So I'm leaning towards B, but not exactly "nothing" is happening to the water molecules. Am I missing something?

 

[Andrew Mason]

3. The attempt at solutions
I think the answer to the first question is B, because the air has no defined velocity and thus there should be no difference in relative velocity whether it's on the ground or in the air. However, I'm not sure if the fact that it rose to the air means that a vertical component is added to the plane's velocity, which would make the resulting velocity 210mph/cos(25), equivalent to 232mph (answer A.)

This is a poor question. The speed relative to a point on the ground is the same as the speed relative to the air, if there is no relative motion between the air and the ground. However, I suspect that they intended the 210 mph to be the horizontal speed of the plane relative to the ground, in which case your second answer would be correct.

As for the second question, I don't think that C is true, because water molecules do not increase in temperature, and therefore speed, during change in state. What I learned in Chemistry is that the energy used during state change is used for breaking their intermolecular bonds. So I'm leaning towards B, but not exactly "nothing" is happening to the water molecules. Am I missing something?

Again, a bad question. Obviously, "nothing" is not correct. I would say that C is the least incorrect. Although the kinetic energy of the molecules remains the same as the ice melts, the kind of motion changes. As ice, the molecules experience vibrational motion only. The bonds between water molecules prevent translational motion so they don't move around. After melting, the molecules have translational motion and can move around.

Good for you for noticing that these questions do not have correct answers.

AM

 

[LowlyPion]

... which would make the resulting velocity 210mph/cos(25), equivalent to 232mph (answer A.)

Yes. I would take speed in air to be the instantaneous rate of change of displacement in air. This includes the z-axis. So ... A.