Unless otherwise stated, in the following problems we assume that the gravitational force is constant with g = 9.81 m/sec2 in the MKS system and g = 32 ft/sec2 in the U.S. Customary System.
If the object in Problem 1 has a mass of 500 kg instead of 5 kg, when will it strike the ground? [Hint: Here the exponential term is too large to ignore. Use Newton’s method to approximate the time t when the object strikes the ground (see Appendix B).]
In this problem, we have to find the time of the object to hit the ground.
The given values are
Mass : m= 500 kg
Gravitational force :g=9.81 m/s2
Proportionality constant b=50 Ns/m
The buoyancy force (while falling downwards) acts downwards the drags force upwards
Therefore m=mg-bv ……………..(1)
The general equation for the force Force= mass x acceleration
Where the acceleration is derivative of the velocity i.e a=
Therefore we will find the time t by integrating the above equation
Now we get
Taking exponential on both sides of the above equation we get