17 Homework 1 Problem Solutions These solutions assume the input data given in the textbook. The data WebAssign gave you will differ from these. 2.1 Distances traveled are ()()()1 1 1 = 80.0 km h 0.500 h 40.0 kmx v t∆ ∆ = = ()()()2 2 2 = 100 km h 0.200 h 20.0 kmx v t∆ ∆ = = ()()()3 3 3 = 40.0 km h 0.750 h 30.0 kmx v t∆ ∆ = = Thus, the total distance traveled is ()40.0 20.0 30.0 km 90.0 kmx∆ = + + =, and the elapsed time is 0.500 h 0.200 h 0.750 h 0.250 h 1.70 ht∆ = + + + =. (a) av90.0 km1.70 hxvt∆= = =∆52.9 km h (b) x∆ =90.0 km (see above) 2.10 The distance traveled by the space shuttle in one orbit is ()()42 Earth’s radius + 200 miles 2 3963 200 mi 2.61 10 miπ π= + = × Thus, the required time is 42.61 10 mi19 800 mi h×=1.32 h 2.15 (a) 10.0 m 02.00 s 0v−= =−5.00 m s (b) ()( )5.00 10.0 m4.00 2.00 sv−= =−2.50 m s− (c) ()( )5.00 5.00 m5.00 4.00 sv−= =−0 (d) ()( )0 5.00 m8.00 7.00 sv− −= =−5.00 m s 1086420246x(m)t(s)1 2 3 4 5 6 7 818 CHAPTER 2 v(m/s)5 10 15 2086422468t(s)2.22 (a) From 0t= to 5.0 st=, 0av00 05.0 s 0v vat t−−= = =− −0 From 5.0 st= to 15 st=, ()av8.0 m s 8.0 m s15 s 5.0 sa− −= =−21.6 m s and from 0t= to 20 st=, ()av8.0 m s 8.0 m s20 s 0a− −= =−20.80 m s (b) At 2.0 st=, the slope of the tangent line to the curve is 0. At 10 st=, the slope of the tangent line is 21.6 m s, and at 18 st=, the slope of the tangent line is 0. 2.26 (a) ( )0av2v vx v t t+ ∆ = ∆ = ∆ becomes ( )02.80m s40.0 m 8.50 s2v+ = , which yields 0v=6.61 m s. (b) 02.80 m s 6.61 m s8.50 sv vat−−= = =∆20.448 m s− 2.45 The velocity of the object when it was 30.0 m above the ground can be determined by applying 2102y v t at∆ = + to the last 1.50 s of the fall. This gives ( ) ( )2021 m30.0 m 1.50 s 9.80 1.50 s2 sv − = + − or 012.6 m sv= − The displacement the object must have undergone, starting from rest, to achieve this velocity at a point 30.0 m above the ground is given by ()2 202v v a y= + ∆ as ( )()( )22 202112.6 m s 08.16 m22 9.80 m sv vya− −−∆ = = = −− The total distance the object drops during the fall is ()()()130.0 mtotaly y∆ = ∆ + − =38.2
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