Please confirm which solution -- Ball is thrown from a tower....

[Julie]

Homework Statement

Question is: Suppose a ball is thrown from a tower 70.0m high with an initial velocity of 3.00 m/s. What will it's speed be after 2.00s? Assume downward is the positive direction and neglect air resistance.

Homework Equations

I have a quiz on Monday in Physics and thought I understood the concepts. My teacher sent us an answer key to some practice questions we are using to study with. His solution differs from mine, and appears to make no sense unless I am missing a step. Could I get someone to clarify which answer is correct?

The Attempt at a Solution

Teacher's Answer:[/B] vf= (-3) + (-9.8)(2) = -42.2 m/s
My Answer: vf= (-3) + (-9.8)(2) = = -22.6

 

[Eclair_de_XII]

Those two expressions are exactly the same; only the right-hand sides differ.

Also, if you treat downwards as the positive direction, then why is the gravitational acceleration negative?

 

[haruspex]

vf= (-3) + (-9.8)(2) = -42.2 m/s

Your teacher typed (-3) + (-9.8)(4) into the calculator. Or if this is from a textbook, maybe an earlier edition had 4s and the answer key was not updated when the question was modified. That is an annoyingly frequent occurrence.

 

[Julie]

Haruspex - thanks so much. Good to know I am not losing my mind. I do have another question since you were so helpful. My original answer was a positive one since the question specifies to assume that downward is the positive direction. I changed it when I realized he is obviously considering down to be negative regardless. Given his answer was wrong, I have less confidence. If question specifies down being positive direction, can correct answer be negative?

 

[gneill]

Hi Julie,

In future, please make sure that your thread title describes the nature of the physics problem being addressed in the post rather than just a plea for help in general. This is so that homework helpers can quickly locate threads that pertain to their area of interest or skill set.

I find the problem statement as written to be rather vague: It doesn't specify whether what direction the ball is initially thrown (it could be up, down, or something else altogether!). The direction would affect the results.

Also, quite often "speed" is interpreted to mean an absolute (positive) scalar quantity. If direction is to be included then it is called "velocity", which is a vector quantity. In this sense, speed is the magnitude of the velocity. You'll often find velocity to be stated in terms of speed and direction, such as "32 m/s to the left".

 

[Julie]

Thanks for the constructive criticism about the posting guidelines. I will remember that in the future. The question was a two part one - the first part indicating that the ball was dropped from a tower - then parameters were changed so it was thrown with a velocity of 3. So, the question assumes the ball was thrown downward. Would both 22.6 downward and -22.6 be correct answers?

 

[gneill]

Would both 22.6 downward and -22.6 be correct answers?

No, since you're told to assume that downwards is the positive direction, and the ball will definitely be moving downwards. So both speed and velocity will have positive values under those circumstances.

Had the ball been moving upwards (for some reason), then its velocity would be negative using that coordinate system. Its speed would still be positive (being the magnitude of the velocity).

 

[Julie]

Thanks so very much. I promise to remember posting guidelines in the future

 

[haruspex]

No, since you're told to assume that downwards is the positive direction, and the ball will definitely be moving downwards. So both speed and velocity will have positive values under those circumstances.

Had the ball been moving upwards (for some reason), then its velocity would be negative using that coordinate system. Its speed would still be positive (being the magnitude of the velocity).

Just to add, since down is positive the acceleration should be +9.8m/s², giving 3+(9.8)2.