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There is a tower of height 20m and a par...

There is a tower of height 20m and a particle is projected up from top of the tower with an initial speed 20m//s. Top of the tower is marked as point A, from where particle is projected. Point of maximum height a denoted as B. When particle reaches the point A during downward journey then we call the same point as C. Point at the bottom of tower is marked as D where particle finally strikes. Acceleration due to gravity `g=10m//s^(2)`
How much time the particle takes to cross the point C after being projected from point A.

A

1s

B

2s

C

3s

D

4s

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem step by step, we will analyze the motion of the particle projected from the top of the tower. ### Step 1: Understand the motion of the particle The particle is projected upwards from point A (top of the tower) with an initial speed of \( u = 20 \, \text{m/s} \). The height of the tower is \( h = 20 \, \text{m} \). The acceleration due to gravity is \( g = 10 \, \text{m/s}^2 \), acting downwards. ### Step 2: Determine the time taken to reach the maximum height (point B) At the maximum height, the final velocity \( v = 0 \). We can use the first equation of motion: \[ v = u - gt \] Substituting the known values: \[ 0 = 20 - 10t \] Solving for \( t \): \[ 10t = 20 \implies t = 2 \, \text{s} \] Thus, the time taken to reach point B from point A is \( 2 \, \text{s} \). ### Step 3: Determine the time taken to return to point A (point C) Since the motion from A to B and from B to C is symmetric, the time taken to return from B to C is also \( 2 \, \text{s} \). ### Step 4: Calculate the total time to cross point C The total time taken to cross point C (which includes the time to go up to B and come back down to C) is: \[ \text{Total time} = \text{Time from A to B} + \text{Time from B to C} = 2 \, \text{s} + 2 \, \text{s} = 4 \, \text{s} \] ### Final Answer The particle takes **4 seconds** to cross point C after being projected from point A. ---
To solve the problem step by step, we will analyze the motion of the particle projected from the top of the tower. ### Step 1: Understand the motion of the particle The particle is projected upwards from point A (top of the tower) with an initial speed of \( u = 20 \, \text{m/s} \). The height of the tower is \( h = 20 \, \text{m} \). The acceleration due to gravity is \( g = 10 \, \text{m/s}^2 \), acting downwards. ### Step 2: Determine the time taken to reach the maximum height (point B) At the maximum height, the final velocity \( v = 0 \). We can use the first equation of motion: \[ ...
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