A man is walking at the rate of 6.5 km/hr towards the foot of a tower 120m high. At what rate is he approaching the top of the tower when he is 5m away from the tower?

Explanation

`y^{2}=x^{2}+(120)^{2}`


`2 y frac{d y}{d t}=2 x frac{d x}{d t}`


`frac{d y}{d t}=frac{x}{y} frac{d x}{d t}`


`frac{d x}{d t}=6.5 frac{{km}}{h r}`


`frac{d y}{d x}=frac{x}{y} times-6.5`


`x=50, y=?`


`y^{2}=x^{2}+(120)^{2}`


`y=sqrt{50^{2}+120^{2}}`


...