Question

A surface ship is moving in a straight line​ (horizontally) at 16 ​km/hr. At the same​ time, an enemy submarine maintains a position directly below the ship while diving at an angle that is 35degrees below the horizontal. How fast is the​ submarine's altitude​ decreasing?

Answer 1

Step-by-step explanation:

It is given that,

A surface ship is moving in a straight line​ (horizontally) at 16 ​km/hr,
`(dx)/(dt)=16\ km/hr`

At the same​ time, an enemy submarine maintains a position directly below the ship while diving at an angle that is 35 degrees below the horizontal,
`\theta=35`

We need to find the rate of decrease of the submarine's altitude i.e.
`(dy)/(dt)`

Using trigonometry,
`cos(35)=(x)/(y)`

`y=sec(35)\ x`

On differentiating the above equation we get :

`(dy)/(dt)=sec(35).(dx)/(dt)`

`(dy)/(dt)=sec(35).* 16`

`(dy)/(dt)=19.53\ km/hr`

So, the submarine's altitude​ is decreasing at the rate of 19.53 km/hr. Hence, this is the required solution.