Thread: Need of help - applying calculus to the physical world

i urgently need help with this question .

- To lift a weight a boy uses a rope 20 metres long thrown over a tree branch which is 6 metres off the ground. He ties the rope around his waist (1 metre off the ground) and walks off at a constant speed of 1ms^(-1). At time, t, let the boy be x metres from the vertical below the weight and let the weight be y metres above the ground.
Find how fast the weight is rising when it is 3 metres above the ground.

Originally Posted by phillychum

i urgently need help with this question .

- To lift a weight a boy uses a rope 20 metres long thrown over a tree branch which is 6 metres off the ground. He ties the rope around his waist (1 metre off the ground) and walks off at a constant speed of 1ms^(-1). At time, t, let the boy be x metres from the vertical below the weight and let the weight be y metres above the ground.
Find how fast the weight is rising when it is 3 metres above the ground.

You can represent vertical motion with dx/dt which will be constant, and vertical motion by dy/dt which is what you want to find, and you can relate x and y using the Pythagorean theorem. (You will use the info that waist is 1 metre off ground and that rope is 20 metres long; assume that tying the rope doesn't shorten it, i.e., following the rope from where the rope meets his waist to where the rope meets the object being lifted is 20 metres.)