Hamilton Williams

04/23/2023 · Primary School

You must get from a point \( P \) on the straight shore of a lake to a stranded swimmer who is 30 m from a point \( Q \) on the shore that is 30 m from you (see figure). If you can swim at a speed of \( 2 \frac{\mathrm{~m}}{\mathrm{~s}} \) and run at a speed of \( 4 \frac{\mathrm{~m}}{\mathrm{~s}} \), at what point along the shore, x meters from Q , should you stop running and start swimming if you want to reach the swimmer in the minimum time? Complete parts (a) through (d) below. B. \( T(x)=\frac{\sqrt{900-x^{2}}}{2}+\frac{(30-x)}{4} \) C. \( T(x)=2 \sqrt{900+x^{2}}+4(30-x) \) D. \( T(x)=4 \sqrt{900+x^{2}}+16(30-x) \) b. Find the critical point of \( T \) on \( (0,30) \). x \( =\square \) (Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression.)