QUESTION 1

An article explains that the locomotion of different-sized animals can be compared when they have V2 the same Froude number, dened as F = a, where v is the animal's velocity, g is the acceleration due to gravity (9.81 mi'secz} and l is the animal's leg length. (a) Different animals change from a trot to a gallop at the same Froude number, roughly 2.56. Find the velocity at which this change occurs for an animal with a leg length of 0.95 m. (b) Ancient footprints of a dinosaur are roughly 0.8 m in diameter, corresponding to a leg length of roughly 3.2 m. By comparing the stride divided by the leg length with that of various modern creatures, it can be determined that the Froude number for this dinosaur is roughly 0.025. How fast was the dinosaur traveling? (a) The velocity at which this animal changes change from a trot to a gallop is mfsec. (Round to the nearest tenth as needed.) The annual number of deer-vehicle accidents for a given area can be estimated by the function A(L,T,U,C) = 53.43 + 0.383L + 0.0015T + 0.0028U - 0.0003C, where A is the estimated number of accidents, L is the road length (in kilometers), T is the total county land area (in hundred- acres (Ha)), U is the urban land area (in hundred-acres), and C is the number of hundred-acres of crop land. Use this formula to estimate the number of deer-vehicle accidents for an area, where L: 262 km, T= 107,495 Ha, U = 31,676 Ha, and C=24,811 Ha. The number of accidents is . (Round to the nearest integer as needed.) Researchers found that the transmission of the COVlD-19 vims is affected by the air temperature and relative humidity according to the formula R = 3.959 - 0.0383T - 0.0221 H, where R is the reproductive number (a quantity measuring the severity of infectiousness), T is the temperature in degrees Celsius, and H is the relative humidity as a percent. Complete parts (a) through (d). (a) Use this formula to estimate the reproductive number for each of the following combinations of temperature and pressure. (i) T = 10, H = 30% (ii) T = 20, H = 30% (iii) T =1o, H = 55% (i) For T =10 and H = 30%, the reproductive number is R = (Round to two decimal places as needed.)