Unit: motion in a plane
Year: 1994 Question#: 62
Question: How many seconds does the ball take to reach the ground?
(1 ) 4.5 s
(2 )20 s
(3 )9.8s
(4 )2.0s
What is this question really asking?
Explanation by: Abby R.
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Answer 1
4.5 s
CORRECT
In this question, you should only consider the vertical motion, because the horizontal motion has nothing to do with the time it takes for the ball to fall. The way that you can figure this out is to consider that the reason the ball is falling. It is being accelerated by gravity. Gravity is the only acceleration the ball experiences, so the time it takes to fall is independent of the horizontal motion. Therefore, you can consider this problem as if it were simply an object falling from rest 100m in the air. (see diagram)
Now, make a list of what you know. You know "s", the distance above the ground, is 100m. You know "a", the acceleration, because it is the acceleration of gravity, 9.8 m/s<sup>2</sup>. You also know V<sub>o</sub>, the original speed, which is 0 because it starts from rest. Keeping in mind that you are trying to find t, pick one of the plane motion equations with s, t, a, and V<sub>o</sub> in it. This equation is:
Plugging in the values and solving for t, you should get 4.5 seconds, the correct answer. Here we take downward to be positive. return to top
Answer 2
20 s
INCORRECT
If you picked this answer, you probably picked it because you noticed the horizontal velocity is 20 m/s. You need to think about the things I explained in Answer 1, not choose an answer quickly because the number is in the diagram. You also might have forgotten to take the square root of the equation:
You could obtain this if you otherwise do the problem correctly using g = 10. meters per second squared. But don't forget to take the square root!
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Answer 3
9.8s
INCORRECT
If you chose this answer, you were probably thinking of the acceleration due to gravity, which is 9.8 meters per second squared. The time to reach the ground is not 9.8s just because the acceleration it is experiences has that numerical value. You should make sure to consider the given values and use equations to reach the answer, not just pick one that looks right. return to top
Answer 4
2.0 s
INCORRECT
If you got this answer, you either wildly guessed or made a calculation error. Make sure you're using the correct equation and that your algebra is correct. Also, don't wildly guess!
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What's this question really asking?
A ball is released from rest 100m above the ground. How long does it take to reach the ground?
This much simpler diagram shows all that you need to consider when calculating the time the ball takes to reach the ground.
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