Initial speed of a thrown/falling stone

In summary, the conversation discusses a problem involving two stones being dropped into a river from a bridge. The initial speed of the second stone is unknown and needs to be calculated using two equations and the acceleration due to gravity. The first equation involves the time it takes for the first stone to hit the water, while the second equation involves the time for the second stone to hit the water. By solving for time in both equations and using the value to find the initial speed, the problem can be solved. However, there is confusion surrounding the use of t1-1 which equals 0 and the concept of time being zero.
  • #1
physics newb
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Another question, I may have more. The reason I'm here is to do some homework due soon. I'm also here to learn, but the sooner the better.

A stone is dropped into a river from a bridge 43.9 m above the water. Another stone is thrown vertically down 1.00 s after the first is dropped. Both stones strike the water at the same time. (a) What is the initial speed of the second stone? (b) Plot velocity vs. time on a graph for each stone, talking zero time as the instant the first stone is released. I'm not sure if you could do a graph on here, but if you could explain in, that would be great!
Thanks!
 
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  • #2
Anyone have ideas to get me started. I'm not sure what to do next.
 
  • #3
Hi, you have 2 unknowns, the time and initial speed, so you need two equations to find them. Remember that the time for the second situation, t2 is given by (t1-1). You need equations of the form x=ut+1/2at^2.
 
  • #4
What does the u stand for in your eqation? How can I get a (acceleration) solved?
 
  • #5
u stands for the initial velocity, maybe you call it [itex]v_{i}[/itex]? a is going to be g=9.81ms^-2, as both stones are falling under gravity. This is the same for both, as after the second stone leaves the person's hand, it will accelerate at g, as the person's hand is no longer providing a force.
 
  • #6
OK, but I still don't know the initial velocity. If I did your equation, would it look like this?
x=u(1.00)+1/2(9.8m/s^2)1.00^2
?
 
  • #7
u is what you're trying to find. That would be part of your second equation, but it should be (t-1.00) not 1.00, where t is the time you get from the first equation (for the stone dropped from rest).
 
  • #8
find the time taken for the first stone to hit the water.
x=u*t+1/2*a*t^2 where u=0ms^-1
then use that value to find time for the second stone. t2=(t1-1)
finally use this same equation again to find u.
x=u*t+1/2*a*t^2
 
  • #9
hello i have a very similar question to this but what i don't understant is t(subscript)1-1 this equals 0... i don't get that?? soo time is zero?
 

1. What is the initial speed of a thrown stone?

The initial speed of a thrown stone is the speed at which the stone is moving when it is first released from the thrower's hand. This speed can vary based on factors such as the force of the throw and the angle at which the stone is released.

2. How is the initial speed of a falling stone calculated?

The initial speed of a falling stone can be calculated using the formula v0 = √(2gh), where v0 is the initial speed, g is the acceleration due to gravity (9.8 m/s2 on Earth), and h is the height from which the stone is dropped.

3. Does air resistance affect the initial speed of a thrown/falling stone?

Yes, air resistance can affect the initial speed of a thrown or falling stone. The presence of air resistance will cause the stone to slow down, resulting in a lower initial speed. However, the degree to which air resistance affects the initial speed will depend on factors such as the shape and size of the stone and the density of the air.

4. How does the initial speed of a thrown stone affect its trajectory?

The initial speed of a thrown stone will affect its trajectory in that a higher initial speed will result in a longer and flatter trajectory, while a lower initial speed will result in a shorter and steeper trajectory. This is because a higher initial speed will give the stone more horizontal velocity, allowing it to travel further before being affected by gravity and falling to the ground.

5. Can the initial speed of a thrown/falling stone be changed?

Yes, the initial speed of a thrown or falling stone can be changed by altering the force of the throw or the height from which the stone is dropped. Additionally, factors such as air resistance and the shape/size of the stone can also affect the initial speed. However, once the stone is released, its initial speed cannot be changed unless acted upon by an external force.

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