Question

(3 points) A ball is dropped from a height of 10 feet and bounces. Suppose that each bounce is 5/8 of the height of the bounce before. Thus, after the ball hits the floor for the first time, it rises to a height of 10 ) = 6.25 feet, etc. (Assume no air resistance.) A. Find an expression for the height, in feet, to which the ball rises after it hits the floor for the nth time: hn = 10(5/8)^n B. Find an expression for the total vertical distance the ball has traveled, in feet, when it hits the floor for the first, second, third and fourth times: first time: D = 10 second time: D = 1 third time: D= fourth time: D= C. Find an expression, in closed form, for the total vertical distance the ball has traveled when it hits the floor for the nth time. Dn=

Answer 1

=625 H nith - Height = 10 ft da first time it asent upto height of 10) = de dad time it went mit went 6-3/8) ft. 23.90625 ft o tymal cong , 1997). 140XD-- DET 3) first time = [108] - and time , 107/105) 4445.) +22547) iled himne 2 104()+43)+2034147) Hit thouse) SF wil come down Before hitting it will travel two times. = 22.5+ 7.8125 2 30.3125 A 4.4 kmé e 30.3125 + 6 10 45° +1047)2) # +35:1953 ft

[ Vertical distance travelled for So sum for ith tiniet s= lot 87181 18) s=10+20 S=1047015) zf** 4*320 +_1209" $=10+2014+633+ +65) Sale+20 597151877 slo te , 41-5')] Loy to Sz lotz$143"] 4 an
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