A falling stone accelerates at a constant rate of 10ms^2. It is dropped from rest down a deep well and 3s later a splash is heard as it hits the water below.(1) How fast will it be moving as it hits the water? (2)What will be its average speed over the three seconds ? (3) how deep is the well ?
I don't. know
find the speed of sound. If it is x m/s, then you have two equal distances.
The distance fallen is s = 5t^2, so the falling time is √(s/5)
The sound takes s/x seconds to come back.
√(s/5) + s/x = 3
So, look up x and do the math for s, the well depth.
The rest then come easily...
Teacher
1) 30m/s
2) 15m/s
3) 45m
To find the answers to these questions, we can apply the equations of motion for uniformly accelerated motion.
1) How fast will it be moving as it hits the water?
To find the final velocity of the stone when it hits the water, we can use the equation:
v = u + at
where:
v = final velocity
u = initial velocity (which is 0 since it is dropped from rest)
a = acceleration
t = time
Given:
u = 0
a = 10 m/s^2
t = 3 seconds
Substituting the given values into the equation, we have:
v = 0 + (10 m/s^2)(3 s)
v = 30 m/s
Therefore, the stone will be moving at 30 m/s as it hits the water.
2) What will be its average speed over the three seconds?
The average speed can be calculated using the equation:
average speed = total distance / total time
In this case, the stone is falling vertically downwards, so its distance is equal to the depth of the well.
To find the distance, we can use the equation of motion for distance in terms of initial velocity, time, and acceleration:
s = ut + (1/2)at^2
where:
s = distance/depth
u = initial velocity
a = acceleration
t = time
Given:
u = 0
a = 10 m/s^2
t = 3 seconds
Substituting the given values into the equation, we have:
s = 0 + (1/2)(10 m/s^2)(3 s)^2
s = 45 m
Therefore, the depth of the well is 45 meters.
Now, we can calculate the average speed over the three seconds:
average speed = total distance / total time
average speed = 45 m / 3 s
average speed = 15 m/s
Therefore, the average speed of the stone over the three seconds is 15 m/s.
3) How deep is the well?
As explained earlier, the depth of the well can be found using the equation:
s = ut + (1/2)at^2
Substituting the given values into this equation, we have:
s = 0 + (1/2)(10 m/s^2)(3 s)^2
s = 45 m
Therefore, the depth of the well is 45 meters.