A falling stone accelerates at a constant rate of 10 m/s square. It is dropped from rest down a deep well, and 3 s later a splash is heard as it hits the water below.
a) How fast will it be moving as it hits the water?
b) What will be its average speed over the three seconds?
c) How deep is the well?
d) What have you assumed about the speed of sound?
(c) if the speed of sound is m m/s, then if the depth of the well is h m,
It takes t seconds to hit the water, where 5t^2 = h, so it takes t=√(h/5) seconds to hit the water
Then, adding up the times,
h/m + t = 3
(d) speed of sound is constant
(a) v = 0-10t = -10√(h/5)
(b) h/t
This gives the avg speed while falling
ignoring the time spent in the water
calculated
good
Student
a b c d
To solve this problem, we can use the equations of motion to find the answers.
a) To find the speed at which the stone hits the water, we need to determine the time it takes for the stone to hit the water. We know that the stone fell for 3 seconds before the splash was heard. The time it takes for the stone to hit the water can be found by rearranging the equation for constant acceleration:
t = √(2s/a)
where t is the time, s is the distance, and a is the acceleration.
Given that the acceleration is 10 m/s^2, and the stone has fallen for 3 seconds, we can substitute these values into the equation:
t = √(2s/10)
3 = √(2s/10)
3^2 = 2s/10
9 = 2s/10
90 = 2s
s = 45
So, the distance the stone falls is 45 meters.
Now, we can use the equation for final velocity to find the speed at which the stone hits the water:
v = u + at
where v is the final velocity, u is the initial velocity (which is zero since the stone was dropped from rest), a is the acceleration, and t is the time.
Given that the acceleration is 10 m/s^2 and the time is 3 seconds, we can substitute these values into the equation:
v = 0 + 10 * 3
v = 30 m/s
Therefore, the stone will be moving at a speed of 30 m/s when it hits the water.
b) The average speed over the three seconds can be found by dividing the total distance traveled by the time taken. In this case, the stone falls a distance of 45 meters in 3 seconds, so the average speed is:
Average speed = distance / time
Average speed = 45 / 3
Average speed = 15 m/s
Therefore, the stone's average speed over the three seconds is 15 m/s.
c) We can find the depth of the well by using the equation of motion:
s = ut + (1/2)at^2
where s is the distance, u is the initial velocity, a is the acceleration, and t is the time.
Since the stone is dropped from rest, the initial velocity is 0. The acceleration is 10 m/s^2 and the time is 3 seconds. Substituting these values into the equation:
s = 0 * 3 + (1/2) * 10 * (3)^2
s = (1/2) * 10 * 9
s = 45
Therefore, the depth of the well is 45 meters.
d) In this problem, we have assumed that the speed of sound is constant. The speed of sound in air is approximately 343 meters per second. However, it's important to note that the actual speed of sound may not always be constant and can vary based on factors such as temperature, humidity, and air pressure.