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Judge a trajectory diagram

A thrown ball is at the very top of its arc. What is its acceleration at that instant?

Here is a diagram of a ball's flight over a wall, with velocity component arrows and acceleration arrows drawn at three points. Diagrams like this are easy to draw and easy to get wrong. Four checks sort the correct ones from the flawed ones.

wallv_xv_yav_xav_xv_ya
A ball's flight over a wall, with velocity component arrows and acceleration arrows at three points. Correct, or flawed?

Every check is a fact you already know. The horizontal velocity never changes. The vertical velocity shrinks to zero at the top and grows after it. At the top the velocity is purely horizontal. And the acceleration is 9.8 m/s² downward at every point.

Check 1: the horizontal velocity arrows are equal at every point. A diagram whose horizontal arrows change length shows the error called changing horizontal arrows.

Check 2: the vertical velocity arrows shrink to zero at the top and grow again after it.

Check 3: at the top there is still a velocity arrow, and it is horizontal. A diagram with no velocity arrow at the top claims the ball stops there: the error called zero velocity at the top.

Check 4: the acceleration arrows are identical at every point, 9.8 m/s² straight down. A diagram that erases the top's acceleration arrow shows zero acceleration at the top. A diagram whose acceleration arrows lean with the curve shows tilted acceleration arrows.

A diagram that passes all four checks is correct. A flawed diagram is named by the first check it fails: changing horizontal arrows, zero velocity at the top, zero acceleration at the top, or tilted acceleration arrows.

Run the four checks on the opening diagram. The horizontal arrows are equal. The vertical arrows shrink to zero at the top and grow after it. The top keeps a horizontal velocity arrow. The acceleration arrows are identical everywhere.

wallv_xv_yav_xav_xv_yaIs the diagram correct?
This diagram passes all four checks, so this diagram is correct.

Now the same diagram with one change: the arrows at the top erased, every other point untouched.

wallv_xv_yav_xv_yaIs the diagram correct?
It fails check 3, so this diagram is flawed: zero velocity at the top.

The same diagram with a different single change: only the top's acceleration arrow removed, the top's velocity arrow kept.

wallv_xv_yav_xv_xv_yaIs the diagram correct?
It fails check 4, so this diagram is flawed: zero acceleration at the top.

The same diagram once more, with the horizontal arrows drawn shorter toward the top and longer after it.

wallv_xv_yav_xav_xv_yaIs the diagram correct?
It fails check 1, so this diagram is flawed: changing horizontal arrows.

A diagram of a softball's arc shows equal horizontal arrows at every point, vertical arrows that shrink to zero at the top and grow after it, and identical downward acceleration arrows everywhere, including the top. Judge the diagram.

Check 1: the horizontal arrows are equal. Pass.

Check 2: the vertical arrows shrink to zero at the top and grow after it. Pass.

Check 3: the top carries a horizontal velocity arrow. Pass.

Check 4: the acceleration arrows are identical and straight down everywhere. Pass.

The diagram passes all four checks, so it is correct.

A diagram of a shot put's flight shows equal horizontal arrows at every point, vertical arrows that shrink to zero at the top and grow after it, and identical downward acceleration arrows at every point. Is the diagram correct?

A diagram of a soccer ball's arc draws, at the very top, no arrows at all. Every other point carries correct arrows. Is the diagram correct?

A diagram of a javelin's flight draws its acceleration arrows leaning with the curve: tilted forward on the way up and tilted backward on the way down. Everything else is correct. Judge the diagram and name the error.

Checks 1 to 3 pass: the velocity arrows are all correct.

Check 4 fails: the acceleration arrows lean with the curve instead of pointing straight down.

The diagram is flawed: tilted acceleration arrows.

A diagram of an arrow's flight is flawed: at the top, the acceleration arrow is missing, though a horizontal velocity arrow is drawn there. Every other point is correct. Which error does the diagram show?

Your turn

A diagram of a thrown ball's arc shows horizontal velocity arrows that get shorter toward the top and longer after it. The other arrows are all correct. The diagram is flawed. Which error does it show?

Four diagrams show the same ball's arc over level ground. Which description matches a correct diagram?

A diagram of a home-run ball's arc draws, at the top, only the downward acceleration arrow and no velocity arrow. Everything else is correct. The diagram is flawed. Which error does it show?