A particle is projected horizontally at 10 ms\(^{-2}\) from the top of a tower 20 M high. Calculate the horizontal distance travelled by the particle when i...
Question 1 Report
A particle is projected horizontally at 10 ms\(^{-2}\) from the top of a tower 20 M high. Calculate the horizontal distance travelled by the particle when it hits the level ground. [g= 10 ms\(^{-2}\)
Answer Details
Vertical motion (to find time of flight). The particle is projected horizontally, so its initial vertical velocity is zero. Falling a height \(h = 20\ \text{m}\):
\[ h = \tfrac{1}{2}g t^{2} \;\Rightarrow\; 20 = \tfrac{1}{2}\times10\times t^{2} \] \[ t^{2} = 4 \;\Rightarrow\; t = 2\ \text{s} \]Horizontal motion (constant velocity). Horizontal speed \(u = 10\ \text{m/s}\), so the horizontal distance (range) is
\[ x = u\,t = 10\times2 = 20\ \text{m} \]The particle strikes the ground 20 m from the foot of the tower.
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