This applet presents simple trajectory problems for students to solve. A cannon fires a projectile horizontally off of a cliff into a bucket. Students must solve for either the height of the cliff, the initial velocity of the projectile, or the distance to the bucket given the other two. The parameters are varied by the applet each time. A short derivation of the correct answer is given if the student enters an incorrect answer.
This is a part of an extensive collection of online tutorials and exercises in introductory physics.
Problem solving for 2D kinematics problems.
Target Student Population:
High school physics students. This also could be useful for helping introductory physics students in college.
Prerequisite Knowledge or Skills:
Kinematics equations and simple algebra.
Type of Material:
Drill and practice
Shockwave plugin required.
Evaluation and Observation
The ability to solve 2D kinematics problems is an important skill for success in introductory physics. This applet focuses on projectile motion. It will allow students to work on this skill through continuing practice and immediate feedback about how to find the correct answer.
The need to solve for any one of the three variables in the problem is a plus.
This simulation does not include the possibility of the initial velocity being at an angle to the horizontal. This would both increase the difficulty of the problems, requiring the solution of a quadratic equation, and broaden somewhat the problems to be solved.
In the questions, velocities are given to six significant figures, seemingly to give nearly integer answers for the height of the cliff or the distance to the bucket. Fortunately, when asking for the velocity, answers given to two or three digits are marked as correct.
For one reviewer, problems that asked for the height of the cliff did not work. The applet marked correct answers as incorrect, even though the answer given by the applet in the solution is identical to that input in the answer box.
Potential Effectiveness as a Teaching Tool
The immediate feedback, and ability to repeatedly answer these questions are positive.
The feedback given for incorrect answers includes a brief derivation that indicates the importance of finding the time-of-flight for the projectile to solve the problem. There is also a link to an extensive, and generally good textual tutorial on projectiles and problem solving.
The applet requires somewhat high precision answers.
While not necessary, the graphics do not accurately simulate the problem.
Because this applet essentially only simulates a single type of problem,
it may not hold the interest of students as long as necessary for them to become proficient.
More emphasis could be given on the fact that all of these, and in fact all 2D trajectory problems, are all the same. Students should be helped to realize that a general approach will solve all these problems.
Ease of Use for Both Students and Faculty
The applet is very simple to use, and the online help is quite satisfactory.
The animation does not show the trajectory of the projectile, although the cliff height and bucket position change with each problem.
When initially started, the applet begins with an incorrect answer, which might confuse some students.