Sliding ladder related rates ( finding velocity at t=1)

Question

A 5m ladder leans against a wall . The bottom of the ladder is 1.5m from the wall at time t=0 and slides away from the wall at a rate pf 0.8m/s. Find the velocity of the top of the ladder at time t=1 

Answer 1

Related rates starts with a formula, in this case the Pythagorean theorem. You the take the derivative implicitly, in terms of time to find the way the rates are related.

 

a² + b² = 5²

 

2a(da/dt) + 2b(db/dt)= 0 is the related rates equation.

 

after 1 second, the ladder slipped .8 m which means at that time, the sides of the triangle are 2.3,b and 5. Using the first equation you can figure out that b = 4.44.

 

So a=2.3, b=4.44 and da/dt=.8. you can now plug this into the related rates equation.

 

2(2.3)(.8) + 2(4.44)(db/dt)=0

db/dt = -8.88/3.68 = - 2.413 m/s

 

Hope this helped.