comparing the surface area of a sphere with its volume and assuming that air resistance is proportional to the square of velocity, it is possible to make a heuristic argument to support the following premise. For similarly shaped objects, terminal velocity varies in proportion to the square root of length. Expressed in the formula below, where L is length, T is terminal velocity, and k is a constant that depends on shape, among other things. This relation can be used to help explain why small mammals easily survive falls that would seriously injure or kill a human. T = kL0.5 (a) A 5 foot woman is 20 times as long as a 3-inch mouse (neglecting the tail). How does the terminal velocity of the woman compare with that of a mouse? Express to 2 decimal places. The terminal velocity of the woman is
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
By comparing the surface area of a sphere with its volume and assuming that air resistance is proportional to the square of velocity, it is possible to make a heuristic argument to support the following premise. For similarly shaped objects, terminal velocity varies in proportion to the square root of length. Expressed in the formula below, where L is length, T is terminal velocity, and k is a constant that depends on shape, among other things. This relation can be used to help explain why small mammals easily survive falls that would seriously injure or kill a human.
(b) If the 5 foot woman has a terminal velocity of 140 miles per hour, what is the terminal velocity of the 3 inch mouse? Express to tenths.
miles per hour
(c) Neglecting the tail, a squirrel is about 6 inches long. What is the terminal velocity of a squirrel? Express to 2 decimal places.
Hint: Refer to part (b).
miles per hour
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