Question Type 7: Finding the related rates between variable given contextual information on their relation Exercises

A ladder of length $10\,\mathrm{m}$ leans against a vertical wall. The base slides away from the wall at $2\,\mathrm{m/s}$. How fast is the top of the ladder sliding down the wall when the base is $6\,\mathrm{m}$ from the wall?

A $5\,\mathrm{m}$ ladder leans against a wall. The top slides down at $1.5\,\mathrm{m/s}$. How fast is the base moving away from the wall when the top is $4\,\mathrm{m}$ above the ground?

A ladder of length $13\,\mathrm{m}$ leans against a wall. The base slides away at $2\,\mathrm{m/s}$. Find the rate at which the top is sliding down when the base is $5\,\mathrm{m}$ from the wall.

A $25\,\mathrm{m}$ ladder slides down. Its base moves away at $4\,\mathrm{m/s}$. Find the rate of change of the area of the right triangle formed by ladder, wall, and ground when the base is $7\,\mathrm{m}$ from the wall.

A ladder of length $10\,\mathrm{m}$ leans against a wall. Its base slides away at $1\,\mathrm{m/s}$. Find the rate of change of the angle $\theta$ between the ladder and the ground when the base is $6\,\mathrm{m}$ from the wall.

A ladder of length $20\,\mathrm{m}$ slides. Its base moves away at $4\,\mathrm{m/s}$. Find the rate of change of the perimeter of the triangle formed by ladder, wall, and ground when the base is $12\,\mathrm{m}$ from the wall.

A ladder of length $13\,\mathrm{m}$ slides with its base moving at $2\,\mathrm{m/s}$. At what distance of the base from the wall is the speed of the top half the speed of the base?

A $15\,\mathrm{m}$ ladder slides down a wall with the base moving away at $3\,\mathrm{m/s}$. Find the rate of change of the angle $\theta$ between the ladder and the wall when the top is $9\,\mathrm{m}$ high.

A $17\,\mathrm{m}$ ladder slides so that the top moves down at $d y/ d t$. Find the rate of change of the angle $\theta$ between ladder and ground in terms of $dy/dt$ when the top is $8\,\mathrm{m}$ above the ground.

A $30\,\mathrm{m}$ ladder slides with its base moving at $2\,\mathrm{m/s}$. Find the rate of change of $\cot\theta$ (where $\theta$ is the angle with the ground) when the base is $18\,\mathrm{m}$ from the wall.

A $20\,\mathrm{m}$ ladder leans against a wall. The base slides away at $3\,\mathrm{m/s}$. Let $\varphi$ be the angle between ladder and wall. Find $d\varphi/dt$ when the base is $12\,\mathrm{m}$ from the wall.

A $13\,\mathrm{m}$ ladder leans against a wall. The angle $\theta$ between ladder and ground decreases at $0.1\,\mathrm{rad/s}$. How fast is the base moving when $\theta=\arccos(5/13)$?