Question 3.4.1: Additional Answer Options

2021 - May/June - Paper 1 - Question 4

Or

Option 2

Upwards as positive:

\mathrm{V}_{\mathrm{f}}=\mathrm{V}_{\mathrm{i}}+\mathrm{a}\Delta\mathrm{t}

0=v_{i}+(-9,8)(1,02)

\mathrm{v}_{\mathrm{i}}=10\mathrm{m}\cdot\mathrm{s}^{-1}(9,996)

Or

Downwards as positive:

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

0=v_{i}+(9,8)(1,02)

v_{i}=-10

v_{i}=10\mathrm{m}\cdot\mathrm{s}^{-1}(9,996)

Or

Option 3

Upwards as positive:

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

-\mathrm{V}=\mathrm{V}+(-9,8)(2,04)

\mathrm{v}=10\mathrm{m}\cdot\mathrm{s}^{-1}(9,996)

Or

Downwards as positive:

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

\mathrm{v}=-\mathrm{v}+(9,8)(2,04)

v=-10

\mathrm{v}=10\mathrm{m}\cdot\mathrm{s}^{-1}(9,996)

Or

Option 4

Upwards as positive:

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

0=v_{i}(2,04)+1/2(-9,8)(2,04)^2

\mathrm{v}_{\mathrm{i}}=10\mathrm{m}\cdot\mathrm{s}^{-1}(9,996)

Or

Downwards as positive:

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

0=v_{i}(2,04)+1/2(9,8)(2,04)^2

v_{i}=-10

v_{i}=10m\cdot s^{-1}(9,996)

Or

Option 5

Upwards as positive:

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

=\left(\frac{v_{i}+0}{2}\right)(1,02)

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

0^2=v_{i}^2+2(-9,8)\left(\frac{v_{i}+0}{2}\right)(1,02)

v_{i}=10m\cdot s^{-1}(9,996)

Or

Downwards as positive:

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

=\left(\frac{v_{i}+0}{2}\right)(1,02)

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

0^2=v_{i}^2+2(9,8)\left(\frac{v_{i}+0}{2}\right)(1,02)

v_{i}=-10m\cdot s^{-1}

v_{i}=10m\cdot s^{-1}(9,996)

Or

Option 6

Upwards as positive:

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

v_{f}=0+(-9,8)(1,02)

\mathrm{v}_{\mathrm{f}}=10\mathrm{~m}\cdot\mathrm{s}^{-1}

\mathrm{v}_{\mathrm{i}}=10\mathrm{~m}\cdot\mathrm{s}^{-1}

Or

Downwards as positive:

\mathrm{V}_{\mathrm{f}}=\mathrm{V}_{\mathrm{i}}+\mathrm{a}\Delta\mathrm{t}

v_{f}=0+(9,8)(1,02)

\mathrm{v}_{\mathrm{f}}=10\mathrm{~m}\cdot\mathrm{s}^{-1}

\mathrm{v}_{\mathrm{i}}=10\mathrm{~m}\cdot\mathrm{s}^{-1}

Or

Option 7

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

\mathrm{mgh}+0=0+1/2\mathrm{mv}^2

(9,8)(5,09796)=1/2v^2

\text{ \lparen2\rparen }(9,8)(5,09796)=v^2

v_{i}=10m\cdot s^{-1}(9,996)

Or

Option 8

W_{\text{net }}=\Delta E_{k}

\mathrm{F}_{\text{net }}\Delta\mathrm{y}\cos\theta=1/2\mathrm{~m}\left(\mathrm{v}_{\mathrm{f}}^2-\mathrm{v}_{\mathrm{i}}^2\right)

\mathrm{ma}\Delta y\cos\theta=1/2m\left(v_{f}{}^2-v_{i}{}^2\right)

(0,06)(9,8)(5,09796)=1/2(0,06)\left(v_{f}^2-0^2\right)

\mathrm{v}_{\mathrm{i}}=10\mathrm{m}\cdot\mathrm{s}^{-1}(9,996)

Or

Option 9

\mathrm{W}_{\mathrm{nc}}=\Delta\mathrm{E}_{\mathrm{p}}+\Delta\mathrm{E}_{\mathrm{k}}

0=mg\left(h_{f}-h_{i}\right)+1/2m\left(v_{f}^2-v_{i}^2\right)

0=(0,06)(9,8)\left(h_{f}-0\right)+1/2(0,06)\left(0^2-v_{i}^2\right)

\mathrm{v}_{\mathrm{i}}=10\mathrm{m}\cdot\mathrm{s}^{-1}(9,996)

Or

Option 10

\mathrm{F}_{\mathrm{net}}\Delta\mathrm{t}=\mathrm{m}\Delta\mathrm{v}

(0,06)(-9,8)(1,02)=(0,06)\left(0-v_{i}\right)

v_{i}=10m\cdot s^{-1}(9,996)

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