A projectile of mass m is shot straight up with initial velocity vo and feels a

Question

A projectile of mass m is shot straight up with initial velocity vo and feels a quadratic air resistance force of the form F =-kv2 , where k=mg/u2 . (k and u are constants and g is the acceleration of gravity.)

a) Find the speed of the projectile at time t while the projectile is still moving upwards. (Hint: you will need to know or calculate an indefinite integral and apply initial conditions.)

b) Take the limit u approaches infinity (that is, k approaches 0) in the above expression and show that it goes over to the standard expression for resistance-free vertical motion.

c) Find the time T at which the projectile reaches its maximum height.(Hint: the result will be of the form of a constant muliplying the tangent of another constant.)

Explanation / Answer

Fnet=?mgv2/u2?mg which leads to

a=?gv2/u2?g

dvdt=?g(v2u2+1)

Solving this differential equation with the initial condition t=0,v0=0 results in

v=utan(?gtu+arctan(v0u))

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