12th grade Related rates worksheet

Related rates

Grade 12 Math Worksheet - Challenge Me

Circle the best answer, or write your answer on the line.

1. 1.

   A 10 m ladder's foot slides away from a wall at 3 m/s; θ is the angle at the ground. Bo finds dθ/dt, in radians per second, when the foot is 8 m out.
2. 2.

   A 5 m ladder's foot slides away from a wall at 1 m/s; θ is the angle at the ground. Esme finds dθ/dt, in radians per second, when the foot is 4 m out.
3. 3.

   A 25 m ladder's foot slides away from a wall at 1 m/s; θ is the angle at the ground. Jun finds dθ/dt, in radians per second, when the foot is 24 m out.
4. 4.

   A 1.5 m robot rolls away from a 6 m lamp post at 2 m/s. Kira finds how fast the robot's shadow gets longer. What is it, in m/s?
5. 5.

   A 1 m robot rolls away from a 5 m lamp post at 3 m/s. Luz finds how fast the robot's shadow gets longer. What is it, in m/s?
6. 6.

   A 2 m robot rolls away from a 8 m lamp post at 1.2 m/s. Milo finds how fast the robot's shadow gets longer. What is it, in m/s?
7. 7.

   A 1 m robot rolls away from a 4 m lamp post at 1.5 m/s. Noah finds how fast the robot's shadow gets longer. What is it, in m/s?
8. 8.

   Water drains from a cylinder of fixed radius 3 m, with V = 9πh. Pia differentiates both sides with respect to time t. Which is right?

   • dV/dt = 9π
   • dV/dt = 6πh · dh/dt
   • V = 9π · dh/dt
   • dV/dt = 9π · dh/dt
9. 9.

   A 10 m ladder slides, with x² + y² = 100. Tala differentiates both sides with respect to time t. Which is right?

   • 2x · dx/dt + 2y · dy/dt = 0
   • 2x · dx/dt + 2y · dy/dt = 100
   • 2x · dx/dt + 2y · dy/dt = 20 · dL/dt
   • 2x + 2y = 0
10. 10.

    A square tile grows, with A = s². Zee differentiates both sides with respect to time t. Which is right?

    • A = 2s · ds/dt
    • dA/dt = 2s · ds/dt
    • dA/dt = 2s
    • dA/dt = s · ds/dt