A stone is thrown vertically upward in air at a velocity of 50 m/s. A frictional drag AV2, where A is a constant and V is the velocity, acts on the stone in the direction opposite to that of the motion. The stone rises until the velocity becomes zero and then accelerates downward to the ground. Its velocity is governed by the following equations, while going upward and while coming down, respectively
where t is time and g is the gravitational acceleration, given as 9.8 m/s2. If A is given as 10−3 m−l , solve the first equation to obtain the time when velocity becomes zero. Using this as the initial condition for the second equation, find the velocity attained by the falling stone in the time taken for the upward motion. Use Euler’s method and vary the time step Δt to ensure that the results are not significantly affected by the step size chosen.
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