2. A container weighs 640 lb. The container will be used to drop supplies into a...

Transcribed Image Text:

2. A container weighs 640 lb. The container will be used to drop supplies into a remote area. Assume the initial velocity of the container is zero as it is dropped from a plane. The container is acted upon by two forces, a force due to gravity from the weight of the container and a force due to air resistance with magnitude k|v|, with k found empirically to be 1 lb/(ft/sec). a) Let v(t) represent the velocity of the container as a function of time t. Write down the differential equation for this falling object. Write the DE in the form = f (t,v). dv dt Fair container b) Find the limiting velocity of the container. c) If the container is likely to burst upon an impact of more than 75 ft/sec, what is the maximum height to which the container can be dropped without likelihood of bursting on impact when it reaches the ground? Fgravity 2. A container weighs 640 lb. The container will be used to drop supplies into a remote area. Assume the initial velocity of the container is zero as it is dropped from a plane. The container is acted upon by two forces, a force due to gravity from the weight of the container and a force due to air resistance with magnitude k|v|, with k found empirically to be 1 lb/(ft/sec). a) Let v(t) represent the velocity of the container as a function of time t. Write down the differential equation for this falling object. Write the DE in the form = f (t,v). dv dt Fair container b) Find the limiting velocity of the container. c) If the container is likely to burst upon an impact of more than 75 ft/sec, what is the maximum height to which the container can be dropped without likelihood of bursting on impact when it reaches the ground? Fgravity