\text { A vector field representing wind speeds is given by } \mathbf{v}=5 x y^{2} \hat{\mathbf{i}}+4 y \hat{\mathbf{j}} \text {. } A walker can take one of two paths between points A(0,0) and B(1,1). Determine which path has more work done by the field? The first path follows y = x2. Find the work done by the field following this path. For path c1, \underline{\mathbf{v}} \bullet d \underline{\mathbf{r}}=( \int_{c 1} \mathbf{v} \bullet d \mathbf{r}= The second path follows y =2. Find the work done by the field following this path. \underline{\mathbf{v}} \bullet d \mathbf{r}=( \int_{c 2} \mathbf{v} \bullet d \underline{\mathbf{r}}= Which path should you take if you want to put in less effort? Path on curve 1-----O Path on curve 2------Either path, effort is the same.

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