Question

Two parallel paths 35 m apart run east-west through the woods. Brooke jogs east on one path at 9 km/h, while Jamail walks west on the other path at 4 km/h. If they pass each other at time t = 0, How far apart are they 5 seconds later? How fast is the distance between them changing at that moment?

Answer 1

Answer:

Explanation:

brooke speed, u = 9 km/h = 2.5 m/s

Jamail speed, v = 4 km/h = 1.11 m/s

Let Booke is at (0, 0) and Jamail is at 35 m. So, at time t, the position of Brooke is (2.5 t , 0 ) and Jamail is (- 1.11 t, 35)

Let l be the distance between them.

$L=\sqrt{\left ( 2.5 t + 1.11 t \right )^{2}+35^{2}} = \sqrt{13.03t^{2}+1225}$

Distance at t = 5 s

$L = \sqrt{13.03\times 5\times 5+1225}$

L = 39.38 m

Differentiate with respect to time

$\frac{dL}{dt}=\frac{t}{\sqrt{13.03t^{2}+1225}}$

Put t = 5 s

$\frac{dL}{dt}=\frac{5}{\sqrt{13.03\times 5\times 5+1225}}$

dL/dt = 0.127 m/s