Question

At a certain point on a heated metal plate, the greatest rate of temperature increase, 3 degrees Celsius per meter, is toward the northeast. If an object at this point moves directly north, at what rate is the temperature increasing?

Answer 1

Explanation:

Formula to determine the rate of temperature increasing will be calculated as follows.

              $D_{u}F = \Delta F.\vec{u}$

                       = $|\Delta F|.|j| cos \theta$

                       = $3.|1|.cos(\frac{\pi}{4})$

                       = $3 \times \frac{1}{\sqrt{2}}$

                       = $\frac{3 \sqrt{2}}{2}$

                       = 2.121

Thus, we can conclude that the rate at which the temperature increasing is 2.121.

Answer 2

Answer:

Explanation:

The rate of temperature increase towards north east is 3 °C/m

So, the component of increase in temperature in north is the component of the increase in temperature towards north east

Desired component = 3 cos 45° = 2.12 °C/m