91Ó°ÊÓ

$$\begin{gathered} \mathrm{A}->\mathrm{speed}=520\mathrm{m}/\mathrm{s},\mathrm{θ}=14.0° \\ \mathrm{B}->\mathrm{speed}=630\mathrm{m}/\mathrm{s},\mathrm{θ}=16.0° \\ \mathrm{C}->\mathrm{speed}=750\mathrm{m}/\mathrm{s},\mathrm{θ}=18.0° \\ \mathrm{D}->\mathrm{speed}=870\mathrm{m}/\mathrm{s},\mathrm{θ}=20.0° \\ \mathrm{E}->\mathrm{speed}=1000\mathrm{m}/\mathrm{s},\mathrm{θ}=22.0° \end{gathered}$$

Projectile motion is the motion of a particle that is launched with an initial velocity. During its flight, the particle’s horizontal acceleration is zero and its vertical acceleration is the free-fall acceleration (Upward is taken to be a positive direction.)

We can use the projectile motion concept to calculate the x- and y-coordinates for different speeds and angles.

Formulae:

The horizontal distance of the body in projectile motion, $\mathrm{x}={\mathrm{V}}_0\mathrm{³¦´Ç²õθ³Ù}$ …(¾±)

The vertical distance of the body in projectile motion, $\mathrm{y}={\mathrm{V}}_0\mathrm{²õ¾\pm ²Ôθ}\mathrm{t}\frac{1}{2}{\mathrm{gt}}^2$ …(¾±¾±)

For launch of A,

The x-coordinate is given using equation (i) as:

$$\begin{gathered} \mathrm{x}=\left(520\mathrm{m}/\mathrm{s}\right)\cos \left(14°\right)\left(20\mathrm{s}\right) \\ =10.1\mathrm{km} \end{gathered}$$

The y-coordinate is given using equation (ii) as:

role="math" localid="1657020170294" $$\begin{gathered} \mathrm{y}=\left(520\mathrm{m}/\mathrm{s}\right)\sin \left(14°\right)\left(20\mathrm{s}\right)-\frac{1}{2}\left(9.8\mathrm{m}/{\mathrm{s}}^2\right){\left(20\mathrm{s}\right)}^2 \\ =0.556\mathrm{km} \end{gathered}$$

For launch of B,

The x-coordinate is given using equation (i) as:

$$\begin{gathered} \mathrm{x}=\left(630\mathrm{m}/\mathrm{s}\right)\cos \left(16°\right)\left(20\mathrm{s}\right) \\ =12.1\mathrm{km} \end{gathered}$$

The y-coordinate is given using equation (ii) as:

$$\begin{gathered} \mathrm{y}=\left(630\mathrm{m}/\mathrm{s}\right)\sin \left(16°\right)\left(20\mathrm{s}\right)-\frac{1}{2}\left(9.8\mathrm{m}/{\mathrm{s}}^2\right){\left(20\mathrm{s}\right)}^2 \\ =1.51\mathrm{km} \end{gathered}$$

For launch of C,

The x-coordinate is given using equation (i) as:

$$\begin{gathered} \mathrm{x}=\left(750\mathrm{m}/\mathrm{s}\right)\cos \left(18°\right)\left(20\mathrm{s}\right) \\ =14.3\mathrm{km} \end{gathered}$$

The y-coordinate is given using equation (ii) as:

$$\begin{gathered} \mathrm{y}=\left(750\mathrm{m}/\mathrm{s}\right)\sin \left(18°\right)\left(20\mathrm{s}\right)-\frac{1}{2}\left(9.8\mathrm{m}/{\mathrm{s}}^2\right){\left(20\mathrm{s}\right)}^2 \\ =2.68\mathrm{km} \end{gathered}$$

For launch of D,

The x-coordinate is given using equation (i) as:

$$\begin{gathered} \mathrm{x}=\left(870\mathrm{m}/\mathrm{s}\right)\cos \left(20°\right)\left(20\mathrm{s}\right) \\ =16.4\mathrm{km} \end{gathered}$$

The y-coordinate is given using equation (ii) as:

$$\begin{gathered} \mathrm{y}=\left(870\mathrm{m}/\mathrm{s}\right)\sin \left(20°\right)\left(20\mathrm{s}\right)-\frac{1}{2}\left(9.8\mathrm{m}/{\mathrm{s}}^2\right){\left(20\mathrm{s}\right)}^2 \\ =3.99\mathrm{km} \end{gathered}$$

For launch of E,

The x-coordinate is given using equation (i) as:

$$\begin{gathered} \mathrm{x}=\left(1000\mathrm{m}/\mathrm{s}\right)\cos \left(22°\right)\left(20\mathrm{s}\right) \\ =18.5\mathrm{km} \end{gathered}$$

The y-coordinate is given using equation (ii) as:

$$\begin{gathered} \mathrm{y}=\left(1000\mathrm{m}/\mathrm{s}\right)\sin \left(22°\right)\left(20\mathrm{s}\right)-\frac{1}{2}\left(9.8\mathrm{m}/{\mathrm{s}}^2\right){\left(20\mathrm{s}\right)}^2 \\ =5.53\mathrm{km} \end{gathered}$$

Hence, we get the x and y co-ordinates for all cases as:

A: (x, y) = (10.1, 0.556)km

B: (x, y) = (12.1, 1.51)km

C: (x, y) = (14.3, 2.68)km

D: (x, y) = (16.4, 3.99)km

E: (x, y) = (18.5, 5.53)km

The plot of x co-ordinates along x axis and y co-ordinates along y axis will be like below.