- #1

tryingtolearn1

- 58

- 5

- Homework Statement
- A block starts at rest and slides down a frictionless plane inclined at an angle ##\theta##. What should ##\theta## be so that the block travels a given horizontal distance in the minimum amount of time?

- Relevant Equations
- $$F=ma$$

When drawing a diagram of the forces acting on the block, I have the following forces: $$\sum F_x = a_x = (g \sin\theta) \cos \theta .$$

Now, I can use the following kinematic equation $$x=vt+\frac{a_xt^2}{2}$$, where $$v=0$$ and $$a_x = (g \sin\theta) \cos \theta$$ $$\therefore \frac{2x}{t^2} = (g \sin\theta) \cos \theta .$$

Now in order to obtain the minimum amount of time, I will need to take the derivative and set it equal to zero but this is where I get stuck and don't know how to proceed?

Now, I can use the following kinematic equation $$x=vt+\frac{a_xt^2}{2}$$, where $$v=0$$ and $$a_x = (g \sin\theta) \cos \theta$$ $$\therefore \frac{2x}{t^2} = (g \sin\theta) \cos \theta .$$

Now in order to obtain the minimum amount of time, I will need to take the derivative and set it equal to zero but this is where I get stuck and don't know how to proceed?