Question

7a. [5] Suppose a steady wind blows northeast with w=. The wind exerts a unit of force for each unit of its velocity. Compute the work done to move an object from the origin to point (10, 10) along a straight line. 7b. |5 Compute the work done to move an object from the origin to point (10, 10) along the parabola y = 2 10

Answer 1

Solution:

we have

$\vec{\text{F}}=10\sqrt{2}\left \langle \frac{1}{\sqrt{2}},\frac{1}{\sqrt{2}} \right \rangle$

r(t) (t, t> ,0 < t < 10

Work Done = / F . dr(t)

/ F (r(t) ) . ґ(t)dt Work Done-

$\text{Work Done}=\int_0^{10}\left \langle 10,10 \right \rangle\cdot \left \langle 1,1 \right \rangle\mathrm{d}t$

$\text{Work Done}=\int_0^{10}20\mathrm{d}t$

Work Done 200