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From a tower of height 400 m, a particle is thrown vertically upwards with a speed of 10 m/s. If the time taken by if to reach the highest point is T then the time taken by the particle to hit the ground is A 20 T B 15 T C 10 T D 5T?
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From a tower of height 400 m, a particle is thrown vertically upwards ...
Answer:
Given: Height of the tower (h) = 400 m, Initial velocity of the particle (u) = 10 m/s, Acceleration due to gravity (g) = 9.8 m/s²
Finding the time taken to reach the highest point:
When the particle is thrown upwards, it moves against the gravity. Hence, the acceleration (a) acting on the particle is given by:
a = -g (as the particle is moving against gravity)
Using the kinematic equation:
v = u + at
where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time taken
At the highest point, the final velocity (v) becomes zero. Hence, we can write:
0 = u - gt
Solving for t, we get:
t = u/g
Substituting the given values, we get:
t = 10/9.8 = 1.02 seconds
Therefore, the time taken by the particle to reach the highest point is 1.02 seconds.
Finding the time taken to hit the ground:
The total time taken by the particle to hit the ground is twice the time taken by it to reach the highest point (as the particle follows the same path while coming down as it did while going up).
Hence, the time taken by the particle to hit the ground is:
2t = 2 x 1.02 = 2.04 seconds
Therefore, the correct option is (A) 20T.
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From a tower of height 400 m, a particle is thrown vertically upwards with a speed of 10 m/s. If the time taken by if to reach the highest point is T then the time taken by the particle to hit the ground is A 20 T B 15 T C 10 T D 5T?
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