Solving for Time to Reach Ground: Calculating Velocity of Sound over 50m

In summary, the speaker used the formula Δd = (Vo + Vf)/2 * t to find the time it took for the ball to hit the ground. They had an initial velocity of 330 m/s and a distance of 50m, and after solving for time, they got 0.15 seconds. The remaining 5.85 seconds was the time the ball was in the air. The confusion about the final velocity was resolved, and the solution was found.
  • #1
Robloxian642
7
4
Homework Statement
A baseball is hit 50 meters. The sound of the ball hitting the ground is heard 6 seconds later. How long did it take for the ball to hit the ground
Relevant Equations
Δd = (Vo + Vf)/2 * t
So I figured that to find how long did the ball take to hit the ground I would have to subtract 6 with the time it took the sound to reach back to the player.

My givens are

Velocity Intial = 330 m/s, speed of sound
Δd = 50m
Velocity Final = 0m/s because sound stops when it reaches the ear?? confused about this one

What I need to find is the time
Δd = (Vo + Vf)/2 * t

50 = 330/2 * t
50 = 165* t
t = 0.303 -- Time it takes to get back to the ear

6 - 0.303 = 5.7

The answer on the back is 5.805

How can I find a solution to this problem, thank you for reading
 
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  • #2
Is the answer in the back 5.85 or 5.805? I think this is just a constant velocity problem using the speed of sound. The sound is not changing its velocity so there isn't an initial and final velocity (or the initial and the final is the same if you want to use that equation). Just one constant velocity. So, you can just use d=v*t (50=330*t). If solving for time, you get 0.15 seconds. So out of the total 6 seconds, only 0.15 seconds was the sound traveling back to your ear. The other 5.85 seconds was the ball in the air.
 
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  • #3
thank you i understand now
 

Related to Solving for Time to Reach Ground: Calculating Velocity of Sound over 50m

1. How do you calculate the velocity of sound over 50m?

To calculate the velocity of sound over 50m, you will need to use the formula v = d/t, where v is the velocity, d is the distance (50m), and t is the time it takes for sound to travel that distance. This will give you the average velocity of sound over 50m.

2. What is the formula for calculating time to reach ground?

The formula for calculating time to reach ground is t = √(2h/g), where t is the time, h is the initial height, and g is the acceleration due to gravity (9.8 m/s²). This formula assumes that the object is dropped from rest and falls freely under the influence of gravity.

3. How does temperature affect the velocity of sound?

Temperature has a direct effect on the velocity of sound. As temperature increases, the velocity of sound also increases. This is because sound waves travel faster in warmer air, as the molecules are moving at a higher speed.

4. What is the unit of measurement for velocity of sound?

The unit of measurement for velocity of sound is meters per second (m/s). This measures the distance that sound travels in one second.

5. How accurate is the calculation for time to reach ground?

The calculation for time to reach ground is highly accurate as long as the initial height and the acceleration due to gravity are known. However, this formula does not take into account air resistance, which can affect the actual time it takes for an object to reach the ground.

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