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).
https://s1.lite.msu.edu/cgi-bin/plot.png?file=kupaemil_msu_1313003849_28535704_plot.data
• The initial speed of N is _____ that of Q.
• The initial speed of P is _____ that of R.
• The time of travel of R is _____ that of P
• The time of travel of N is _____ that of Q
• The initial speed of Q is _____ that of P.
• The time of travel of P is _____ that of N.

its either less than, greater than, or equal to

Explanation / Answer

So we know that the 4 graphs represent the paths of 4 objects, two moving along frictionless incline planes, and 2 in projectile motion. What we can see is that N and Q are the ones in free fall (notice how their vertical vs. horizontal graphs are that of parabolic motion, thus suggesting they are given an initial speed, but the force of gravity decelerates them to the point that their direction would be reversed at the 9 m mark, or the apex of their motion, and they would fall down in their motion continued), and that P and R are the ones on frictionless incline planes because they have a constant velocity throughout their journey to the 9m mark (thus suggesting they were dragged up the plane at a constant velocity). With that in mind, let's answer your questions: The initial speed of N is less than that of Q (notice how N's slope locally at the start, think first derivative if you have learned that concept, is larger than Q's; however, look at what you are comparing, vertical vs. horizontal distance. If you wanted two objects to reach the same height, but one to do so in a greater horizontal distance, you would change the angle of the shot, in this case Q, and have to increase its speed to still get it to the necessary height) The initial speed of P is equal to that of R (Again, look at the slopes, however look as well at what you are comparing. You are comparing vertical to horizontal distance, thus suggesting from the graph that P's incline was longer than R's but in no way suggesting that one was dragged at a faster rate than the other, assuming the same force was used for both) The time of travel of R is less than that of P (Going back to slopes, R was dragged at a rate of more altitude per horizontal distance, implying that it traveled quicker than P if the same force was used to drag each respective block) The time of travel of N is less than that of Q (We know that the object Q would stay in the air longer because it is shot over a greater horizontal distance, thus it also takes a longer time to reach the apex of its journey, correct?) The initial speed of Q is great than that of P (Looking at the slopes, Q was given an initial velocity which shot it 2 m up for 1 m horizontal distance, whereas the speed of P suggests it was traveling at a constant velocity of 1 m up per 1 m across) The time travel of P is less than that of N (Looking at the horizontal distances covered, it took P a greater distance to reach 9 m, and considering we know gravity was working on N to decelerate it, we can assume N decelerated quickly to reach the apex of its motion because it did so in much less horizontal distance) Let me know if my explanations and solutions are adequate!

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.