A shape that covers an area A and has a uniform height h has a volume V = Ah. (a) Show that V = Ah is dimensionally correct.
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- A rectangular airstrip measures 32.50 m by 290 m, with the width measured more accurately than the length. Find the area (in m2), taking into account significant figures.Consider the physical quantities m, s, v, a, t, and r with dimensions [m] = M, [s] = L, [v] = LT–1, [a] = LT–2, [t] = T, and [r] = L. Assuming each of the following equations is dimensionally consistent, find the dimension of the quantity on the left-hand side of the equation: (a) F = ma; (b) K = 0.5mv2; (c) p = mv; (d) W = mas; (e) L = mvr.(a) A pyramid has a height of 462 ft and its base covers an area of 12.0 acres (see figure below). The volume of a pyramid is given by the expression covers V = Bh, 3 where B is the area of the base and h is the height. Find the volume of this pyramid in cubic meters. (1 acre = ! 1 A FI 2.27e6 Enter a number. (b) What If? If the height of the pyramid were increased to 520 ft and the height to base area ratio of the pyramid were kept constant, by what percentage would the volume of the pyramid increase? % m³ N 2 Q F2 W S X # www 3 20 F3 E D $ 4 C @ 000 DOD F4 R F % 5 V F5 T G MacBook Air 6 F6 Y B & SN 7 H 8 F7 U :43,560 ft²) N +00 * 8 J DII FB 1 ( 9 M K FO O O < ge A F10 P : I + { OUR TEACHER [ F12 11 delete
- A new landowner has a triangular piece of flat land she wishes to fence. Starting at the west corner, she measures the first side to be 84 m long and the next to be 102 m. These sides are represented as displacement vectors A and B in the figure. She then calculates the length of the third side C. What is her result (in meters)?A hopskip is a (fictional) unit of length equal to 1.5 meters (1 hs = 1.5 m). The volume of the Earth’s oceans is estimated to be ~ 1.3X 10^24cm . Use dimensional analysis to express the volume of the Earth’s oceans in hs^3.