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 of 25 m from the foo...
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 of 25 m from the foot of the tower. Calculate the height of the tower. = 10 ms\(^{-2}\)]
Answer Details
For a projectile launched horizontally, the horizontal and vertical motions are independent.
Step 1 - find the time of flight from the horizontal motion. Horizontally the speed is constant at \(u = 4\,\text{m s}^{-1}\):
\[ R = u\,t \;\Rightarrow\; 25 = 4t \;\Rightarrow\; t = 6.25\,\text{s}. \]
Step 2 - find the height from the vertical motion. The stone starts with zero vertical velocity and falls freely:
\[ h = \tfrac{1}{2} g t^{2} = \tfrac{1}{2}\times10\times(6.25)^{2}. \]
\[ h = 5\times39.06 \approx 195.3\,\text{m}. \]
The height of the tower is approximately 195.3 m.
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