Explanations & Calculations
i)
Apply S = u t + 1 2 a t 2 \small S= ut +\frac{1}{2}at^2 S = u t + 2 1 a t 2 for the projectile's vertical motion, downwards ↓ \downarrow ↓ 100 = 1 2 g T 2 \qquad\qquad
\begin{aligned}
\small 100&=\small \frac{1}{2}gT^2
\end{aligned} 100 = 2 1 g T 2
ii)
Apply the same formula for its horizontal motion. → s = u t + 1 2 a t 2 R = 330 m s − 1 × T \qquad\qquad
\begin{aligned}
\small \to s&=\small ut+\frac{1}{2}at^2\\
\small R&=\small 330\,ms^{-1}\times T
\end{aligned} → s R = u t + 2 1 a t 2 = 330 m s − 1 × T
iii)
To find the vertical velocity component at the landing, apply v = u + a t \small v=u+at v = u + a t for its vertical motion, again downward. ↓ v y = 0 + g T → v y = g T \qquad\qquad
\begin{aligned}
\small \downarrow v_y&=\small 0+gT\to v_y=gT
\end{aligned} ↓ v y = 0 + g T → v y = g T
Then the velocity at the landing is the compound value of both horizontal & vertical velocities. V = v x 2 + v y 2 = 33 0 2 + g 2 T 2 \qquad\qquad
\begin{aligned}
\small V&=\small \sqrt{v_x^2+v_y^2}\\
&=\small \sqrt{330^2+g^2T^2}
\end{aligned} V = v x 2 + v y 2 = 33 0 2 + g 2 T 2
iv)
The angle at which it would be landing is tan θ = v y v x θ = tan − 1 [ g T 330 ] \qquad\qquad
\begin{aligned}
\small \tan\theta&=\small \frac{v_y}{v_x}\\
\small \theta&=\small \tan^{-1}\bigg[\frac{gT}{330}\bigg]
\end{aligned} tan θ θ = v x v y = tan − 1 [ 330 g T ]
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