A stone projected horizontally from the top of a tower with a speed of 4 ms\(^{-1}\) lands on the level ground at a horizontal distance 25 m from the foot o...
Question 1 Report
A stone projected horizontally from the top of a tower with a speed of 4 ms\(^{-1}\) lands on the level ground at a horizontal distance 25 m from the foot of the tower. Calculate the height of the tower. g = 10 ms\(^{-2}\)]
Answer Details
Horizontal projection: initial horizontal speed \(u=4\,\text{ms}^{-1}\), horizontal range \(x=25\,\text{m}\), \(g=10\,\text{ms}^{-2}\).
Horizontal motion (constant velocity) gives the time of flight:
\[ x=ut\Rightarrow t=\frac{x}{u}=\frac{25}{4}=6.25\,\text{s} \]Vertical motion (falling from rest, initial vertical velocity zero) gives the height of the tower:
\[ h=\tfrac{1}{2}gt^2=\tfrac{1}{2}\times10\times(6.25)^2=5\times39.06=195.3\,\text{m} \]So the tower is about \(195\,\text{m}\) high.
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