Question

A bowling ball is dropped from a boat so that it strikes the surface of a lake at a speed of 25 ft/s. Assuming the ball experiences a downward Accel of a = 10 - .9v^2when in the water, determine the velocity of the ball when it strikes the bottom of the lake, 30 ft below surface.

Answer 1

From the given data, the acceleration is, a=10-0.9v2 = k (c? – v?) Here, k = 0.9 ft-1 c? 10 0.9 62 =11.1111f? /s? C=3.33 ft/s The distance traveled is, X-Xo = 30 ft The derived form of acceleration, chy way = klc* _v2) = -k(v2-(2) do -=-kdy "TV2 -c?)

Integrate the above equation, (10 (92-c*)) = -2(x=80) (1n(v2_cº) =-2(x=6) I --2(x=80) v2 -c? = e(+2{x-vo) (Vg2 -ca) v2 = {l_24/v=o) (172 -cº)+c? v2 = -2409730 A) (( 25 ft/s) -11.1111 f? /s?) +11.1111 ft /s? v2 =11.1111 ft²/s2 v=3.33 ft/s