Question

A shell is fired with a horizontal velocity in the positive x-direction from the top of an 80m high cliff. The shell strikes the ground 1330 m from the base of the cliff. What is the initial speed of the shell? (Take g = 10 m/s²)

Moderate

Solution

The initial velocity in the y-direction is zero.
$\begin{array}{l} y - y_{0} = u_{y} t + \frac{1}{2} a_{y} t^{2} \\ \Rightarrow (- 80) - 0 = (0) t - \frac{1}{2} (10) t^{2} \Rightarrow t = \sqrt{\frac{80}{5}} = 4 s \end{array}$
The horizontal displacement is 1330 m. If the initial speed is v₀, then
$v_{0} t = 1330 \Rightarrow v_{0} = \frac{1330}{4} = 332 .5 m / s$

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