2022 A/L Physics Past Paper · Question 09 (English Medium)

Answer: (2) Only (C) is true.

What the question asks

We want: which of the statements (A), (B) and (C) are true for a ball that flies from $A$ to $B$, at the same level, with no air resistance.

What each letter means:

$v_x$ ($\text{m s}^{-1}$): horizontal part of the velocity.

$v_y$ ($\text{m s}^{-1}$): vertical part of the velocity.

$E_k$ ($\text{J}$): kinetic energy of the ball.

$m$ ($\text{kg}$): mass of the ball.

$h$ ($\text{m}$): height of the ball above the level of $A$.

$g$ ($\text{m s}^{-2}$): acceleration due to gravity.

Relevant theory

Vertical component of velocity decreases.

This decreases until it reaches zero. After that, due to the gravitational force acting on the body, vertical component of the velocity gradually increases in downward direction until it hits the ground.

Horizontal component remains constant. In determining the velocity of the ball at a given time using vector addition, it is clear that its trajectory is a parabola.

If in a certain process the conservation of energy takes place only between kinetic energy and potential energy, then in that process the sum of the kinetic energy and the potential energy remains a constant. This is the principle of conservation of mechanical energy.

Reading the options

The options are combinations of (A), (B) and (C).

We test each statement on its own.

For example, think of one fielder who throws a cricket ball to a team-mate standing at the same height.

While the ball climbs it slows down. At the top it has not stopped. It is still moving forward.

Then it speeds up as it falls. When the team-mate catches it at the height where it left the hand, it is as fast as it was at the start. But now it is going down, and at the start it was going up.

Gravity pulls only straight down. So it changes only the vertical part of the motion.

$$v_x = \text{constant}$$

In words: the horizontal part of the velocity never changes.

$$E_k + mgh = \text{constant}$$

In words: the kinetic energy and the potential energy together stay the same.

The same height means the same $mgh$. So the kinetic energy is the same too.

Reasoning and calculation

The velocity of the ball at the maximum height of the path is zero.

At the top $v_y = 0$, but $v_x$ is still there. The ball is moving sideways, so its velocity is not zero.

A

The velocity of the ball at point $B$ is equal to the velocity at point $A$.

At $B$ the ball is at the height of $A$, so it is as fast. But at $A$ it moves upward and at $B$ it moves downward. $v_y$ has changed sign, so the velocity is a different vector.

B

The kinetic energy of the ball at point $B$ is equal to the kinetic energy at point $A$.

Only gravity acts, so $E_k + mgh$ stays constant. $A$ and $B$ are at the same height, so $mgh$ is the same at both. So $E_k$ is the same.

C

Statement (A) is false, because the horizontal part of the velocity never becomes zero.

Statement (B) is false, because the direction at $B$ is different from the direction at $A$.

Statement (C) is true, because the two points are at the same height.

So only (C) is true.

Why the other options fail

Statement (A) is false, because the ball still moves sideways at the top. Statement (C) is true.

Statement (B) is false. The vertical part of the velocity is upward at $A$ and downward at $B$.

Statement (A) is false, because the horizontal part of the velocity stays the same all the way.

Statements (A) and (B) are false, so not all three are true.

Conclusion

Only statement (C) is true. (A) and (B) are false.

The answer is (2).

Velocity has a size and a direction. Speed has only a size.

At the same height the speed and the kinetic energy are the same. The direction may not be.

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