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A ball is dropped from a bridge at a height of 176.4 m over a river. After 2 s, a second ball is thrown straight downwards. What should be the initial velocity of the second ball so that both hit the water simultaneously ?
  • a)
    2.45 m/s
  • b)
    49 m/s
  • c)
    14.5 m/s
  • d)
    24.5 m/s
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
A ball is dropped from a bridge at a height of 176.4 m over a river. A...
Given: Height of the bridge (h) = 176.4 m, time taken by the first ball to hit the water (t) = 2 s

To find: Initial velocity of the second ball (u)

We can use the equations of motion to solve this problem.

Equation of motion for a body under free fall is:

h = ut + (1/2)gt^2

where u is the initial velocity, g is acceleration due to gravity (-9.8 m/s^2).

For the first ball, h = 176.4 m and t = 2 s, so we can find u1:

176.4 = u1(2) + (1/2)(-9.8)(2)^2
u1 = 39.2 m/s

So, the initial velocity of the first ball is 39.2 m/s.

Now, for the second ball, we want both balls to hit the water simultaneously. So, the time taken by the second ball to hit the water should be the same as that of the first ball, i.e., 2 s.

Using the same equation of motion, we can find u2:

h = u2t + (1/2)gt^2
176.4 = u2(2) + (1/2)(-9.8)(2)^2
u2 = 24.5 m/s

So, the initial velocity of the second ball should be 24.5 m/s.

Therefore, the correct answer is option (d) 24.5 m/s.
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A ball is dropped from a bridge at a height of 176.4 m over a river. A...
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A ball is dropped from a bridge at a height of 176.4 m over a river. After 2 s, a second ball is thrown straight downwards. What should be the initial velocity of the second ball so that both hit the water simultaneously ?a) 2.45 m/s b) 49 m/s c) 14.5 m/s d) 24.5 m/s Correct answer is option 'D'. Can you explain this answer?
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