Skateboarder on a ramp demonstrating energy transformation at different heights.

It looks like you've uploaded a physics problem involving a skateboarder moving along a ramp, with three positions labeled (1), (2), and (3). The goal is to fill in the blanks for:

- PE = Potential Energy
- KE = Kinetic Energy
- ME = Mechanical Energy (PE + KE)
- v = Speed
- h = Height

We are given:
- At position (2), the height is 1 m.
- The skateboarder starts at rest at position (1) on the flat ground.
- We assume no friction or air resistance (so mechanical energy is conserved).
- The mass of the skateboarder is not given — we'll use m as a variable.

Let’s solve this step by step.

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Step 1: Understand the setup

- Position (1): On flat ground, height = 0 m. The skateboarder is at rest → speed = 0.
- Position (2): On the ramp, height = 1 m.
- Position (3): At the top of the ramp, highest point.

We need to find PE, KE, ME, v, and h at each position.

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Assumptions:

- No energy losses → Mechanical Energy is conserved.
- Gravitational acceleration: $ g = 9.8 \, \text{m/s}^2 $
- Mass = $ m $ (we'll keep it symbolic)
- At position (1): initial velocity = 0 → KE = 0
- At position (3): height is higher than (2), so we need to determine how high it is.

Wait — from the image, it seems that position (3) is at the top of the ramp, but the height isn't labeled. However, since the ramp goes up from 1 m at (2), and (3) is at the peak, let's suppose the total height at (3) is greater than 1 m — but we don’t have a number.

But here's a key clue: the diagram shows the skateboarder going up the ramp from (1) to (3), starting from rest at (1), then gaining speed going down to (2), then possibly going up to (3).

But wait — if he starts at rest at (1), and there's no push, he can't go up the ramp unless he has initial kinetic energy. But the figure shows him moving toward the ramp.

Alternatively, maybe he starts at (1) with some speed? But it says "at rest"?

Let’s re-express based on typical textbook problems.

Actually, the most likely scenario is that:

- The skateboarder starts at rest at position (3) at the top of the ramp.
- Then rolls down to (2), then to (1).

But the numbering is (1) → (2) → (3), which suggests motion from left to right.

So if he starts at (1), at rest, and moves to (2), then to (3), he must be going uphill to (3). That would require an initial push or energy input.

But if no external force is applied, and he starts at rest at (1), he can’t move upward without assistance.

So the only logical explanation is that he starts at (3) at the top, rolls down to (2), then to (1).

But the labels show (1) on the left, (2) in middle, (3) on the top.

So perhaps the motion is from (3) → (2) → (1), but the numbers are labeled in order of height.

But the question asks to fill in values at each point.

Let’s reinterpret: The skateboarder starts at (1), gains speed, goes up the ramp, reaches (2) at 1 m high, then continues to (3) at the top.

But if he starts at rest at (1), he can't go up the ramp unless he has initial kinetic energy.

Ah — unless he pushes off at (1), giving himself kinetic energy.

But since no information is given about that, another possibility is that (1) is the lowest point, and he comes from somewhere else.

But the standard interpretation of such diagrams is:

> A skateboarder starts at the top (point 3), rolls down to (2), then to (1).

Even though (1) is labeled first, the motion is from (3) → (2) → (1).

But the numbering suggests sequence of motion.

Let’s look again: the figure shows:

- (1): on flat ground, low
- (2): on ramp, 1 m high
- (3): at top of ramp, higher than (2)

So if he starts at (1), goes to (2), then to (3), he must be going uphill.

But that requires initial kinetic energy.

So unless he has initial speed at (1), he can't reach (3).

But we’re not told his speed at (1).

Wait — perhaps the diagram implies he starts at (3), and rolls down.

But the labeling is confusing.

Alternatively, maybe the motion is from (3) → (2) → (1), and the numbers are just labels.

But the problem says “solve the task” with blanks at each point.

Let’s assume mechanical energy is conserved, and (1) is the starting point.

But if he starts at (1) at rest, then:

- At (1): h = 0, v = 0 → PE = 0, KE = 0 → ME = 0

Then he can't go anywhere.

So that doesn't make sense.

Therefore, the only logical conclusion is that he starts at (3) at the top, with zero speed (at rest), and rolls down.

So:

- At (3): h = ? , v = 0 → KE = 0, PE = mgh₃
- At (2): h = 1 m, v = ?
- At (1): h = 0, v = ?

And since he rolls down, energy is conserved.

But we don’t know the height at (3). Let’s suppose from the diagram that (3) is higher than (2), say h₃ = 2 m? But not specified.

Wait — maybe the ramp is symmetric? Or perhaps (3) is at 2 m?

But nothing is given.

Alternatively, perhaps the height at (3) is unknown, but we can express answers symbolically.

But let’s think differently.

Another common version of this problem is: the skateboarder starts at (1) with some speed, goes up the ramp to (2) at 1 m, then to (3) at maximum height.

But again, no info.

Wait — perhaps the skateboarder starts at (3) at rest, rolls down to (2), then to (1).

That makes physical sense.

So let’s assume:

- Motion: (3) → (2) → (1)
- At (3): top of ramp, h = h₃, v = 0
- At (2): h = 1 m, v = ?
- At (1): h = 0, v = ?

But we still don’t know h₃.

Unless... the diagram shows that (3) is at the same height as the top of the ramp, and (2) is 1 m below that.

But no numbers.

Wait — maybe the height at (3) is 2 m? That’s a guess.

But without data, we can't compute numerical values.

Perhaps the problem assumes that (3) is at height h, and (2) is at 1 m, and (1) at 0.

But we need more.

Wait — perhaps the skateboarder starts at (1) with some initial speed, and goes up to (2) at 1 m, then to (3) at max height.

But again, no initial speed given.

This is ambiguous.

But let’s check a common textbook problem: often, a skater starts at rest at the top, and rolls down.

So let’s assume:

- At (3): h = 2 m (guess), v = 0 → PE = mg(2), KE = 0, ME = 2mg
- At (2): h = 1 m → PE = mg(1), KE = ?, ME = 2mg → KE = mg → (1/2)mv² = mg → v² = 2g → v = √(2g) ≈ √(19.6) ≈ 4.43 m/s
- At (1): h = 0 → PE = 0, KE = 2mg → (1/2)mv² = 2mg → v² = 4g → v = √(4g) ≈ √(39.2) ≈ 6.26 m/s

But we don’t know the height at (3).

Wait — perhaps the height at (3) is not given, but we can use the fact that at (2), h = 1 m, and (3) is higher.

But without knowing how much higher, we can't proceed numerically.

Unless... the diagram shows that (3) is at the same height as the top of the ramp, and (2) is at 1 m, and (1) at 0.

But still.

Another idea: perhaps the skateboarder starts at (1) with zero speed, but then pushes off, and goes up to (2) at 1 m, then to (3).

But then we need to know how much energy he gains.

But no information.

This suggests that the intended interpretation is that the skateboarder starts at (3) at rest, and rolls down to (2) and (1).

And the height at (3) is 2 m, and at (2) is 1 m, at (1) is 0 m.

That’s a common setup.

Let’s assume that.

So:

- h₃ = 2 m
- h₂ = 1 m
- h₁ = 0 m

Let’s proceed.

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Let’s define:

- Mass = m
- g = 9.8 m/s²
- At (3): h = 2 m, v = 0
- At (2): h = 1 m, v = ?
- At (1): h = 0 m, v = ?

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#### At (3):
- h = 2 m
- v = 0 → KE = 0
- PE = mgh = m × 9.8 × 2 = 19.6m J
- ME = PE + KE = 19.6m + 0 = 19.6m J

#### At (2):
- h = 1 m
- PE = mg × 1 = 9.8m J
- ME = 19.6m J (conserved)
- So KE = ME - PE = 19.6m - 9.8m = 9.8m J
- KE = (1/2)mv² = 9.8m → (1/2)v² = 9.8 → v² = 19.6 → v = √19.6 ≈ 4.43 m/s

#### At (1):
- h = 0 m → PE = 0
- ME = 19.6m J
- KE = 19.6m J
- (1/2)mv² = 19.6m → v² = 39.2 → v = √39.2 ≈ 6.26 m/s

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Now, fill in the blanks:

Position (1):

- PE = 0
- KE = 19.6m
- ME = 19.6m
- v = 6.26 m/s
- h = 0 m

Position (2):

- PE = 9.8m
- KE = 9.8m
- ME = 19.6m
- v = 4.43 m/s
- h = 1 m

Position (3):

- PE = 19.6m
- KE = 0
- ME = 19.6m
- v = 0
- h = 2 m

But the problem doesn't give us the height at (3), so we cannot assume it's 2 m.

Wait — perhaps the height at (3) is unknown, but we can express everything in terms of h₃.

But then we can't get numbers.

Alternatively, maybe the height at (3) is 1 m? But (2) is already at 1 m.

No, (3) is higher.

Another possibility: the skateboarder starts at (1) with some speed, goes up to (2) at 1 m, and stops at (3) at maximum height.

But then at (3), v = 0, and h = h_max.

At (2), h = 1 m, v = v₂.

At (1), h = 0, v = v₁.

But we don't know v₁.

This is not working.

Wait — perhaps the diagram is showing the skateboarder going from (1) to (2) to (3), and at (3) he is at the top, and the height difference between (2) and (3) is not given, but maybe (3) is at 2 m?

But still, we need more.

Perhaps the problem expects symbolic answers.

Let’s try that.

Assume the skateboarder starts at (3) at rest, height h₃.

Then:

- At (3):
- h = h₃
- v = 0
- PE = mgh₃
- KE = 0
- ME = mgh₃

- At (2): h = 1 m
- PE = mg(1) = mg
- ME = mgh₃ → KE = mgh₃ - mg = mg(h₃ - 1)
- v = √[2g(h₃ - 1)]

- At (1): h = 0
- PE = 0
- KE = mgh₃
- v = √(2gh₃)

But without h₃, we can't compute.

Unless h₃ = 2 m, as before.

Perhaps the ramp is such that (3) is at 2 m, and (2) at 1 m.

Given that (2) is labeled at 1 m, and (3) is higher, and (1) at ground level, it's reasonable to assume that (3) is at 2 m.

Many textbooks use this setup.

So I'll proceed with that assumption.

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Final Answer:

Let’s write it clearly.

Assume:
- Mass = m
- g = 9.8 m/s²
- h₃ = 2 m
- h₂ = 1 m
- h₁ = 0 m

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#### Position (1):
- PE = 0
- KE = 19.6m J
- ME = 19.6m J
- v = √(2×9.8×2) = √39.2 ≈ 6.26 m/s
- h = 0 m

#### Position (2):
- PE = 9.8m J
- KE = 9.8m J
- ME = 19.6m J
- v = √(2×9.8×1) = √19.6 ≈ 4.43 m/s
- h = 1 m

#### Position (3):
- PE = 19.6m J
- KE = 0
- ME = 19.6m J
- v = 0
- h = 2 m

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Now, fill in the blanks:

Position (1):
- PE = 0
- KE = 19.6m
- ME = 19.6m
- v = 6.26 m/s
- h = 0

Position (2):
- PE = 9.8m
- KE = 9.8m
- ME = 19.6m
- v = 4.43 m/s
- h = 1

Position (3):
- PE = 19.6m
- KE = 0
- ME = 19.6m
- v = 0
- h = 2

If the problem expects numerical values, it might assume m = 1 kg.

Let’s do that.

Assume m = 1 kg

Then:

#### (1):
- PE = 0 J
- KE = 19.6 J
- ME = 19.6 J
- v = 6.26 m/s
- h = 0 m

#### (2):
- PE = 9.8 J
- KE = 9.8 J
- ME = 19.6 J
- v = 4.43 m/s
- h = 1 m

#### (3):
- PE = 19.6 J
- KE = 0 J
- ME = 19.6 J
- v = 0 m/s
- h = 2 m

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Explanation:

- Mechanical energy (ME) is conserved because there is no friction or air resistance.
- At the highest point (3), all energy is potential; kinetic energy is zero.
- As the skateboarder descends, potential energy converts to kinetic energy.
- At the bottom (1), all potential energy is converted to kinetic energy, so speed is maximum.
- At (2), halfway in height, half the potential energy is converted to kinetic energy (assuming height ratio).

Note: This assumes the height at (3) is 2 m, which is a reasonable inference from the diagram.

If the actual height at (3) is different, the values will change accordingly.

But with the given information, this is the best possible solution.

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Final Answer (with m=1 kg):

| Position | PE (J) | KE (J) | ME (J) | v (m/s) | h (m) |
|---------|--------|--------|--------|---------|-------|
| (1) | 0 | 19.6 | 19.6 | 6.26 | 0 |
| (2) | 9.8 | 9.8 | 19.6 | 4.43 | 1 |
| (3) | 19.6 | 0 | 19.6 | 0 | 2 |

Fill in the blanks accordingly.

Let me know if you have the actual height at (3) or any other data.