A heat seeking missile is programmed to head in the direction in which the tempe
ID: 3288928 • Letter: A
Question
A heat seeking missile is programmed to head in the direction in which the temperature T increases most rapidly. The missile's sensors have collected the following data: Straight ahead T increases at a rate of 1(degree/m), 30 degrees to the left T increases at a rate of 0.5 (degrees/m), 45 degrees above the forward direction, T decreases at a rate of 0.2 (degrees/m) In which direction should the missile head, and at what rate is the temperature increasing in this direction? Give the direction as a unit vector.
Explanation / Answer
Straight ahead: 1*(j)
30 degrees to the left : 0.5*(-1.7/2 i + 1/2 j) [sqrt3 = 1.7, sqrt2 = 1.4]
45 degrees above the forward direction: -0.2(1.4/2 j + 1.4/2 k)
Average =-0.43 i +1.11 j - 0.14 k
Unit vector :[-0.43 i +1.11 j - 0.14 k]/1.436
Rate of increase in temp = magnitude = 2.045