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

Mathematics

Amelia Hobbs

9 May, 20:32

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

+1

Answers (1)

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Nehemiah Mahoney · Answer 1

A = 10 - 0.8vv = d/ta = change in velocity / change in time

v1 = 16.5 fps, t1 = 0, d1 = 0 v2 = y fps, t2 = 3, d2 = X

10 - 0.8 (d2/3) = (16.5 - 0) / (0-3) 10 - 0.8 (d2/3) = 16.5/-3d2 = 58.125 feet

v2 = 58.125/3 v2 = 19.375 fps