Question 3.2.3: Additional Answer Options

2022 - November - Paper 1 - Question 3

Option 1

Upwards as positive:

Part 1

A-D:

v_{f}^2=v_{i}^2+2a\Delta y

v_{f}^2=(12)^2+2(-9,8)(-23,1)

\mathrm{v}_{f}=24,43\mathrm{~m}\cdot\mathrm{s}^{-1}

Or

C-D:

v_{f}^2=v_{i}^2+2a\Delta y

v_{f}^2=(-12)^2+(2)(-9,8)(-23,1)

\mathrm{v}_{\mathrm{f}}=24,43\mathrm{~m}\cdot\mathrm{s}^{-1}

Or

D-G:

v_{f}^2=v_{i}^2+2a\Delta y

(-25,18)^2=\left(v_{i}\right)^2+2(-9,8)(-1,9)

\mathrm{v}_{\mathrm{i}}=24,43\mathrm{~m}\cdot\mathrm{s}^{-1}

Or

B-D:

v_{f}^2=v_{i}^2+2a\Delta y

v_{f}^2=0+2(-9,8)(-30,447)

v_{f}=24,43\mathrm{~m}\cdot\mathrm{s}^{-1}

Or

D-G:

\mathrm{E}_{\text{\lparen mech top })}=\mathrm{E}_{\text{\lparen mech bottom })}

\left(E_{p}+E_{k}\right)_{\text{top}}=\left(E_{p}+E_{k}\right)_{\text{bottom }}

\left(\mathrm{mgh}+1/2\mathrm{mv}^2\right)_{\text{top}}=\left(\mathrm{mgh}+1/2\mathrm{mv}^2\right)_{\text{bottom}}

m(9,8)(1,9)+1/2m\left(v_{i}\right)^2=0+1/2m(25,18)^2

\mathrm{v}_{\mathrm{i}}=24,43\mathrm{~m}\cdot\mathrm{s}^{-1}

Part 2

D-G:

v_{f}=v_{i}+a\Delta t

-25,18=-24,43+(-9,8)\Delta t

\Delta t=0,08\mathrm{~s}

Or

D-G:

\Delta y=v_{i}\Delta t+1/2a\Delta t^2

-1,9=-24,43\Delta t+1/2(-9,8)\Delta t^2

\Delta\mathrm{t}=0,08\mathrm{~s}

Or

D-G:

\Delta y=\left(\frac{\mathrm{v}_{\mathrm{i}}+\mathrm{v}_{\mathrm{f}}}{2}\right)\Delta\mathrm{t}

-1,9=\left(\frac{-24,43-25,18}{2}\right)\Delta t

\Delta t=0,08

Or

Downwards as positive:

Part 1

A-D:

v_{f}^2=v_{i}^2+2a\Delta y

v_{f}^2=(-12)^2+2(9,8)(23,1)

\mathrm{v}_{\mathrm{i}}=24,43\mathrm{~m}\cdot\mathrm{s}^{-1}

Or

C-D:

v_{f}^2=v_{i}^2+2a\Delta y

v_{f}^2=(12)^2+(2)(9,8)(23,1)

\mathrm{v}_{\mathrm{i}}=24,43\mathrm{~m}\cdot\mathrm{s}^{-1}

Or

D-G:

v_{f}^2=v_{i}^2+2a\Delta y

(25,18)^2=\left(v_{i}\right)^2+2(9,8)(1,9)

\mathrm{v}_{\mathrm{i}}=24,43\mathrm{~m}\cdot\mathrm{s}^{-1}

Or

B-D:

v_{f}^2=v_{i}^2+2a\Delta y

v_{f}^2=0+2(9,8)(30,447)

\mathrm{v}_{\mathrm{i}}=24,43\mathrm{~m}\cdot\mathrm{s}^{-1}

Or

D-G:

E_{(\text{mech top\rparen}}=E_{\text{\lparen mech bottom\rparen}}

\left(E_{p}+E_{k}\right)_{\text{top }}=\left(E_{p}+E_{k}\right)_{\text{bottom}}

\left(\mathrm{mgh}+1/2\mathrm{mv}^2\right)_{\text{top }}=\left(\mathrm{mgh}+1/2\mathrm{mv}^2\right)_{\text{bot}}

m(9,8)(1,9)+1/2m\left(v_{i}\right)^2=0+1/2m(25,18)^2

\mathrm{v}_{\mathrm{i}}=24,43\mathrm{~m}\cdot\mathrm{s}^{-1}

Part 2

D-G:

v_{f}=v_{i}+a\Delta t

25,18=24,43+(9,8)\Delta t

\Delta\mathrm{t}=0,08\mathrm{~s}

Or

D-G:

\Delta y=v_{i}\Delta t+1/2a\Delta t^2

1,9=24,43\Delta t+1/2(9,8)\Delta t^2

\Delta\mathrm{t}=0,08\mathrm{~s}

Or

D-G:

\Delta\mathrm{y}=\left(\frac{v_{\mathrm{i}}+v_{\mathrm{f}}}{2}\right)\Delta\mathrm{t}

1,9=\left(\frac{24,43+25,18}{2}\right)\Delta t

\Delta\mathrm{t}=0,08\mathrm{~s}

Or

Option 2

Upwards as positive:

A-G:

v_{f}=v_{\mathrm{i}}+a\Delta t

-25.18=12+(-9,8)\Delta t

\Delta\mathrm{t}=3,79\mathrm{~s}

A-D:

\Delta\mathrm{y}=\mathrm{v}_{\mathrm{i}}\Delta\mathrm{t}+\frac12\mathrm{a}\Delta\mathrm{t}^2

-23,1=(12)\Delta t+1/2(-9,8)\Delta t^2

\Delta\mathrm{t}=3,72\mathrm{~s}

D-G:

3,79-3,72=0,07\mathrm{~s}

Or

Downwards as positive:

A-G:

v_{f}=v_{i}+a\Delta t

25,18=-12+(9,8)\Delta t

\Delta\mathrm{t}=3,79\mathrm{~s}

A-D:

\Delta y=v_{i}\Delta t+\frac12a\Delta t^2

23,1=(-12)\Delta t+1/2(9,8)\Delta t^2

\Delta t=3,72\mathrm{~s}

D-G:

3,79-3,72=0,07\mathrm{~s}

Or

Option 3

Upwards as positive:

C-G:

v_{f}=v_{i}+a\Delta t

-25,18=-12+(-9,8)\Delta t

\Delta\mathrm{t}=1,34\mathrm{~s}

C-D:

\Delta\mathrm{y}=\mathrm{v}_{\mathrm{i}}\Delta\mathrm{t}+\frac12\mathrm{a}\Delta\mathrm{t}^2

-23,1=(-12)\Delta t+1/2(-9,8)\Delta t^2

\Delta t=1,27\mathrm{~s}

D-G:

1,34-1,27=0,07\mathrm{~s}

Or

Downwards as positive:

C-G:

v_{f}=v_{i}+a\Delta t

25,18=12+(9,8)\Delta t

\Delta t=1,34\mathrm{~s}

C-D:

\Delta\mathrm{y}=\mathrm{v}_{\mathrm{i}}\Delta\mathrm{t}+\frac12\mathrm{a}\Delta\mathrm{t}^2

23,1=(12)\Delta t+1/2(9,8)\Delta t^2

\Delta t=1,27s

D-G:

1,34-1,27=0,07\mathrm{~s}

Or

Option 4

Upwards as positive:

G-D:

\Delta y=v_{i}\Delta t+1/2a\Delta t^2

1,9=25,18\Delta t+1/2(-9,8)\Delta t^2

\Delta\mathrm{t}=0,08\mathrm{s}\quad(0,077\mathrm{s})

Or

Downwards as positive:

G-D:

\Delta y=v_{i}\Delta t+1/2a\Delta t^2

-1,9=-25,18\Delta t+1/2(9,8)\Delta t^2

\Delta t=0,08\mathrm{s}\quad(0,077\mathrm{s})

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