(a) Assume the equation describes the motion of a particular object, with having the dimension of length and having the dimension of time. Determine the dimensions of the constants A and B .
(b) Determine the dimensions of the derivative .
(a) The dimensions of the constants A and B are and respectively.
(b) The dimension of the derivative equation is .
Adimensional analysis is used to measure the dimensions of any physical quantity, which has no fixed values.Similarly, the dimensions of a constant valued parameter can be determined by using the dimensions of the variable physical quantities.
Write the expression for the motion of the object in terms of the time physical variable.
Here, x is the motion of the object, t is the time, and A, B are the constant parameters.
The dimension of the motion of the object x is the dimension of the length L.
The dimension of time t is T.
Replace L for x and T for t in equation (1).
Here, each term on theright-hand side must be equal to left hand side individually.
Therefore, the dimensions of the constants A and B are and respectively.
Write the derivative expression of equation (1).
Replace T for t , for A and for B in the above equation.
Therefore, the dimension of the derivative equation is .
Hence, the dimensions for the constant parameters A and B and the derivative equation are , and respectively.
A woman wishing to know the height of a mountain measures the angle of elevation of the mountaintop as . After walking closer to the mountain on level ground, she finds the angle to be .
(a)Draw a picture of the problem, neglecting the height of the woman’s eyes above the ground. Hint: Use two triangles.
(b)Using the symbol to represent the mountain height and the symbol to represent the woman’s original distance from the mountain, label the picture.
(c) Using the labelled picture, write two trigonometric equations relating the two selected variables.
(d) Find the height .
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