The labeled graphs below represent the upward trajectories of 4 bodies, two slid

Question

The labeled graphs below represent the upward trajectories of 4 bodies, two sliding upwards on frictionless inclines and two in free flight. Note that all 4 bodies reach the same maximum height (9 meters) after traveling from the same initial elevation (0 m). dynamically generated plot

• The initial speed of R is that of N.

• The time of travel of Q is that of P

• The time of travel of P is that of R.

• The time of travel of R is that of N

• The initial speed of Q is that of P.

• The initial speed of R is that of P.

Great than, equal to, or less than

Explanation / Answer

1)Time R>Time N will have same Kinetic energy (so same initial vel) by R have to travel greater distance. (assuming plane continues beyond trajectory shown and hence zero final velocity.)

2)Will be same (due to same vertical velocity)

3)  dy/dx = (dy/dt)/(dx/dt)

dy/dx = Vy/Vx

.greater than

Because they have the same average velocity (as each experiences uniform acceleration) but R has further to go

4) . Speed R=Speed N already discussed

5) greater than

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

6)  Will be same (due to same vertical velocity)

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