What Force Keeps a Body Moving at Constant Velocity on a Horizontal Surface?

[Amith2006]

Sir,
Please say whether these 2 problems are right.
1) A body of mass 2kg moving on a horizontal surface with an initial velocity of 4 m/sec comes to rest after 2 seconds. If one wants to keep this moving on the same surface with same velocity, what is the force that is needed to be applied?
I solved it in the following way:
Acceleration = (0 – 4)/2
= -2m/sec^2
Retarding force = mass x retardation
= 2 x 2
= 4 Newton
So if a force equal to the retarding force is applied, the body will move with a constant velocity of 4 m/sec^2. But the book answer is 2 Newton. What is your opinion Sir?

2) A splash is heard 4.28 seconds after a stone is dropped into a well 78.4 meters deep. What is the velocity of sound?
I solved it in the following way:
Time taken by the stone to reach the well = [2H/g]^1/2
(Here H is depth of well & g = 9.8 m/sec^2)
= 4 seconds
Time taken by sound to reach the observer = 4.28 – 4
= 0.28 seconds
Velocity of sound = 78.4/0.28
= 280 m/sec
But the book answer is 341 m/sec. What is your opinion?I think the book answer is wrong.

 

[abercrombiems02]

for the first problem i also get an acceleration of 2 m/s^2
since sum F = 0, then it should follow that F = m*a = 4 N
The book must have a typo

for the second problem it also looks like you solved the problem correctly.
While speed typically does travel around 340 m/s at standard atmospheric conditions, the answer does come out to 280 m/s with the numbers they have given you. What text is this anyways?

 

[kyle8921]

The calculation and reasoning for both problems seem to be correct. In the first problem, the retarding force should indeed be equal to the mass x acceleration, which in this case is 4 Newtons. In the second problem, the calculation for the velocity of sound also seems to be correct. The book may have made a mistake in their calculation or may have used a different value for the acceleration due to gravity. As a scientist, it is important to always double check calculations and sources to ensure accuracy. If you are confident in your calculations, then your answers are most likely correct.