Solving initial velocity for falling object

In summary, two stones are dropped from a 65 m high bridge, with the second stone thrown 2 seconds later. Both stones are heard hitting the water at the same time. Using the equation d=vi*t+1/2at^2, the time of fall for the first stone can be calculated to be 5.2 seconds. To make the complete journey, the second stone must also take 5.2 seconds. By substituting t=5.2 into the relevant equation, the initial velocity of the second stone can be solved for. The speed of sound is irrelevant in this scenario.
  • #1
heythere1010
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Homework Statement


A stone is dropped from a bridge that is 65 m high. A second stone is thrown downwards 2 seconds later. Both the stones are heard hitting the water at the same time. The speed of sound is a constant 343 m/s. What is the initial velocity of the second stone.

Homework Equations


d=vi*t+1/2at^2

The Attempt at a Solution


65=0+1/2(-9.8)(t)^2

I know t-2 is used for the time of the second stone. I don't know which equations to use to make them equal.
 
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  • #2
Your Relevant equation should suffice.

What value did you get for the time of fall for the first stone? So what must be the time (numeric value) that the second stone has to make the complete journey?
 
  • #3
gneill said:
Your Relevant equation should suffice.

What value did you get for the time of fall for the first stone? So what must be the time (numeric value) that the second stone has to make the complete journey?
5.2. Do I just sub it into the second equation with t-2 and solve for initial velocity?
 
  • #4
heythere1010 said:
5.2. Do I just sub it into the second equation with t-2 and solve for initial velocity?
Sure.
 
  • #5
haruspex said:
Sure.
So the speed of sound is irrelevant?
 
  • #6
heythere1010 said:
So the speed of sound is irrelevant?
The sounds of hitting the water were heard at the same time. Did they hit the water at the same time?
 
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1. What is initial velocity?

Initial velocity is the velocity of an object at the beginning of its motion.

2. How do I calculate initial velocity for a falling object?

To calculate initial velocity for a falling object, you can use the formula v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration due to gravity (usually -9.8 m/s²), and t is the time the object has been falling.

3. What if I don't know the acceleration due to gravity?

The acceleration due to gravity is a constant value of -9.8 m/s² on Earth. However, if you are on a different planet or in a different environment, you can look up the specific acceleration due to gravity for that location and use it in the formula to calculate initial velocity.

4. Can initial velocity be negative?

Yes, initial velocity can be negative. A negative initial velocity indicates that the object is moving downwards at the beginning of its motion.

5. How does air resistance affect the initial velocity of a falling object?

Air resistance can decrease the initial velocity of a falling object. This is because air resistance acts in the opposite direction of the object's motion, causing it to slow down. However, for most practical purposes, the effects of air resistance can be ignored when calculating initial velocity.

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