The labeled graphs below represent the upward trajectories of 4 bodies, two slid
ID: 1420806 • Letter: T
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).
• The time of travel of Q is.........that of P
• The time of travel of R is........... to that of P.
• The initial speed of P is ............that of Q.
• The initial speed of N is............that of R.
• The time of travel of R is............ that of N
• The initial speed of R is.............that of P
Explanation / Answer
As the graphs are of y vs. x, each simply shows the shape of the path followed by each body.
R is sliding up a steep incline and R is sliding up a less steep incline.
Q and P follow parabolic trajectories - i.e they are simple projectiles.
N and R must each start with a the same kinetic energy as they have zero kinetic energy at 9m. All of their KE is turned to PE.
Q and P are must have equal vertical components of initial velocity to reach the same height. They will reach 9m after the same times, as the vertical motion of projectiles with the same initial vertical components of velocity are identical. However P has a bigger horizontal component of velocity than Q - so P travels further in the time needed to reach max height.
(A)The time of travel of Q is.........that of P
equal to
They have the same vertical velocity component but Q has a smaller horizontal component as explained above. So the initial speed (magnitude of initial velocity) of Q is smaller than P's.
(B)he time of travel of R is........... to that of P.
greater than P
(C)The initial speed of P is ............that of Q.
They have the same vertical velocity component but Q has a smaller horizontal component as explained above. So the initial speed (magnitude of initial velocity) of Q is smaller than P's.
(D)The initial speed of N is............that of R.
equal to as they will have the same initial kinetic energy
(E)The time of travel of R is............ that of N
greater than
Because they have the same average velocity (as each experiences uniform acceleration) but R has further to go
(F)The initial speed of R is.............that of P
less than P
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