A stone is dropped from the top of a tower travels 25m in the last second of itsmotion. If 210 /g m s height of the tower isA) 54m B) 45m C) 25m D) 64m
Question
A stone is dropped from the top of a tower travels 25m in the last second of itsmotion. If 210 /g m s height of the tower isA) 54m B) 45m C) 25m D) 64m
Solution
The problem is about free fall motion. We know that the distance covered by an object under gravity in t seconds is given by the equation:
h = 1/2 * g * t^2
where:
- h is the height,
- g is the acceleration due to gravity (which is approximately 9.8 m/s^2), and
- t is the time.
From the problem, we know that the stone travels 25m in the last second. We can use this information to find the total time of the fall.
Let's assume that the total time of the fall is T seconds. Then, the time 't' is (T-1) seconds. We can write the equation as:
25 = 1/2 * g * (T-1)^2
Given that g = 210/22 m/s^2, we can substitute this value into the equation:
25 = 1/2 * (210/22) * (T-1)^2
Solving this equation gives T = 5 seconds.
Now, we can find the height of the tower by substituting T = 5 seconds into the equation h = 1/2 * g * T^2:
h = 1/2 * (210/22) * 5^2
Solving this gives h = 225/2 = 112.5 m.
Therefore, none of the options A) 54m B) 45m C) 25m D) 64m are correct. The height of the tower is 112.5 m.
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