Four paths concepts? (Calc-based Physics 1)
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Four paths concepts? (Calc-based Physics 1)

[From: ] [author: ] [Date: 12-06-22] [Hit: ]
_____________Q4. equal toExplained above._____________Q5. less thanQs initial speed was just sufficient to give it the kinetic energy needed to reach 9mBut Ns initial vertical component of velocity was just sufficient to give it the kinetic energy needed to reach 9m AND it had a horizontal velocity component. So N had more total kinetic energy than Q. SoQ was slower than N_____________Q6 less thanThe time of travel for N is the time to reach max height.......
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Q1. greater than

Because they have the same average velocity (as each experiences uniform acceleration) but Q has further to go
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Q2. equal to

As explained above - they have the same initial kinetic energy.
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Q3. less than

They have the same vertical velocity component but N has a smaller horizontal component as explained above. So the initial speed (magnitude of initial velocity) of N is smaller than R's.
_____________
Q4. equal to

Explained above.
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Q5. less than

Q's initial speed was just sufficient to give it the kinetic energy needed to reach 9m
But N's initial vertical component of velocity was just sufficient to give it the kinetic energy needed to reach 9m AND it had a horizontal velocity component. So N had more total kinetic energy than Q. So Q was slower than N
_____________
Q6 less than

The time of travel for N is the time to reach max height. Considering vertical motion only, since h = ½gt², t = √[(2h/g].

The time of travel of Q can be calculated using height change and the vertical component of acceleration; this will be gsin(θ) where θ is the angle of inclination to the horizontal. So t = √[2h/(gsin(θ))]
Since sin(θ)<1 it follows that √[2h/(gsin(θ))] is more than √[2h/g]. So the time for N is less than the time for Q.

There's probably a simpler explanation but that illustrates one way of thinking about it.

I think my answers are correct - but can't guarantee them.
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