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) 10 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Relative horizontal position x, (m) The initial speed of Q is greater than that of N The time of travel of Ris greater than that of P The initial speed of P is less than T that of R The time of travel of P is equal to that of Q The initial speed of P is that of Q The time of travel of N is that of Q HER Tries 0/12

Explanation / Answer

We can use conservation of energy and linear motion equations

all 4 bodies were shifted by same height

Here Q and N are free flight so

from conservation of energy

initial vertical speed is equal to final potential energy. So both objects have same vertical speed.

But horizontally N has travelled more than Q.

Hence speed of Q is less than N.

For inclines: Total kinetic energy was converted into potential energy so both P and R have same initial speed but P has travelled more than R so the travel time of R is less than P.

Travelling time of P is greater than Q

Initial speed of P is less than Q

The time of traveling of N is equal to Q

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