A ball is dropped from a boat so that it strikes the surface of a lake with a speed of 16.5 fps. While in the water the ball experiences an acceleration of a=10−0.8v, where a and v are expressed in fps^2 and fps respectively. Knowing the ball takes 3 sec to reach the bottom of the lake, determine the following:
a. the depth of the lake
b. the speed of the ball when it hits the bottom of the lake

Question

A ball is dropped from a boat so that it strikes the surface of a lake with a speed of 16.5 fps. While in the water the ball experiences an acceleration of a=10−0.8v, where a and v are expressed in fps^2 and fps respectively. Knowing the ball takes 3 sec to reach the bottom of the lake, determine the following:
a. the depth of the lake
b. the speed of the ball when it hits the bottom of the lake

schrodingers_cat · Answer

Well you have a resistive force proportinal to your velocity so have to solve the differential equation

dv/dt = 10 - 0.8v

schrodingers_cat · Answer

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