Mathematics Homework Solutions
Problem
#92143

Trigonometry Word Problems : Displacement and Power

1. The displacement of a body is given by, s = 4sin (t + 30degrees), and a force acting upon the body is given by, F = 7sin (t - 60degrees). If the energy of the motion, E, at time t is the product Fs, show that E = -14 cos (2t - 30 degrees).

2. The instantaneous current and voltage in an electric circuit are given by
i = I cos 50pi*t
v = V cos (50pi*t + pi/6)
Determine an expression for the instantaneous power in the circuit, p = iv, as the sum of two cosines.

3. If I is 3mA and V is 5 V, calculate the maximum value of p, giving the answer in watts correct to three significant figures, and the first positive value of t at which it occurs.

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Trigonometry.doc
Trigonometry Problems

1. The displacement of a body is given by, s = 4sin (t + 30degrees), and
a force acting upon the body is given by, F = 7sin (t - 60degrees). If
the energy of the motion, E, at time t is the product Fs, show that E =
-14 cos (2t - 30 degrees).

2. The instantaneous current and voltage in an electric circuit are
given by

i = I cos 50pi*t

v = V cos (50pi*t + pi/6)

Determine an expression for the instantaneous power in the circuit, p =
iv, as the sum of two cosines.

3. If I is 3mA and V is 5 V, calculate the maximum value of p, giving
the answer in watts correct to three significant figures, and the first
positive value of t at which it occurs.

Solution Summary

Displacement and Power are investigated.

Solution
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