Unit: Motion in a Plane
Year: 1997 Question#: 62
Question: Projectiles are fired from different angles with the same initial speed of 14 meters per second. The graph below shows the range of the projectiles as a function of the original angle of inclination to the ground, neglecting air resistance.
The graph shows that the range of the projectiles is:
(1 ) the same for all angles
(2 ) the same for angles of 20 and 80
(3 ) greatest for an angle of 45
(4 ) greatest for an angle of 90
What is this question really asking?
Explanation by: Julie D.
[ Return to question menu ]
Answer 1
the same for all angles
INCORRECT
The range is shown on the y-axis. Therefore the y-value of a point is the distance the projectile went at a certain angle (the x-value of the point). If the projectile had the same range at all angles, all the y-values would be equal and the graph would be a horizontal line.
return to top
Answer 2
the same for angles of 20 and 80
INCORRECT
For the range to be the same at both 20 and 80 , the y-values (which represent the range) would have to be equal for the x-values of 20 and 80 . A close look at the graph shows that the y-value for 20 is approximately 13, and the y-value for 80 is approximately 7, which are not equal. return to top
Answer 3
greatest for an angle of 45
CORRECT
The graph has a maximum at the x-value of 45 . The range corresponding to this angle is 20m, which is the largest y-value on the graph.
return to top
Answer 4
greatest for an angle of 90
INCORRECT
The largest x-value on the graph is 90 , however, it is the largest y-value that the question is asking for. If the projectile is launched at 90 , it goes straight up and straight back down; it does not move at all horizontally. The range is zero. return to top
What's this question really asking?
The question is asking whether or not you can read a graph. It is easy to confuse the graph with a picture of the progectile's motion. In this case, the x-axis is the angle at which it is fired, not the distance it goes, which is the range. The y-values are the range, not the height. Before you start a problem with a graph, make sure you understand what is graphed on each axis. return to top
