IMAT 2016 Q59 [Projected Ball]

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A ball is projected vertically upwards and then falls back to its original position.

Once projected, the ball experiences only a single force, downwards, due to a constant gravitational field strength of 10 N/kg.

Here are three statements about the ball:

  1. When the ball is moving upwards it loses kinetic energy and gains potential energy.
  2. The magnitude of the ball’s acceleration increases as it falls.
  3. No vertical forces act on the ball when it is at its maximum height

Which of the statement(s) is/are correct?

A. 2 and 3 only
B. none of them
C. 1 and 2 only
D. 3 only
E. 1 only

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Using the key words from this question, namely being a “vertically projected ball”, we can formulate our own statements about this system -stating what we know before verifying the mentioned answers.

For a vertically projected ball, it is true that:

A. At it’s maximum height, vertical forces act on the ball. Gravity for example, working downwards.

B. Hence, the acceleration of the ball must be constant going downwards, as it moves at a constant gravitational acceleration of 10m/s^2.

C. As the ball shoots upwards, it must gain Gravitational Potential Energy (GPE).

D. When it shoots upwards, it must eventually slow down- meaning it loses kinetic energy.

What we can now do, is refute the question’s statements using our own.

Statement 1 must be true, as it closely matches our reasoning D and C.

Statement 2 is false, and is refuted by our reasoning B.

Statement 3 is false, as it is refuted by our reasoning A.

Making our final answer Statement 1 only, E.

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