DIFFERENTIAL EQUATIONS - PLEASE SHOW ALL WORK AND WRITE LEGIBLY A ball with mass
ID: 1608995 • Letter: D
Question
DIFFERENTIAL EQUATIONS - PLEASE SHOW ALL WORK AND WRITE LEGIBLY
A ball with mass m kg is dropped from the roof of a building H meter high. There is a force due to air resistance with a magnitude of 0.l v^2, where the velocity v is measured in m/sec. Write down the differential equation and initial conditions that describe the motion of the ball. Write the DE in the form: dv/dt = f(t, v), and clearly identify your reference frame in terms of the direction of motion (+ vs. -). Assume the mass is 0.25 kg and the building is 30 meter high. Find the time required for the velocity of the ball to reach 4 m/sec.Explanation / Answer
b)
as per the eauation of motion:
v = u +at
v=4 m/s
u =0
g = 9.8 m/s2
t= 0.408 seconds
a.)
the net foce acting on the ball is :
1. gravital pull = mg in favour of motion here
2. drag force = 0.1v2 in upword direction
net acceleration = (g -0.1v2/m)
dv/dt = (g -0.1v2/m)
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