Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ ¹ ² ³ °
 

You are not logged in. #1 20131202 13:27:25
Convex MirrorA body is moving towards a convex mirror with speed v. Is the speed of the image equal to v? 'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.' 'God exists because Mathematics is consistent, and the devil exists because we cannot prove it' 'Who are you to judge everything?' Alokananda #2 20131202 18:58:09
Re: Convex Mirrorhi Agnishom, You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #3 20131202 23:11:00
Re: Convex MirrorI already did that but I was wondering if someone had a better answer. 'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.' 'God exists because Mathematics is consistent, and the devil exists because we cannot prove it' 'Who are you to judge everything?' Alokananda #4 20131202 23:51:57
Re: Convex Mirror
So it seems that the speed of movement is not linear. Your answer is good. If you want a formula it will take a little more thought. You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #5 20131203 06:23:19
Re: Convex Mirrorhi Agnishom, According to Wiki, a convex mirror is considered to have a negative focal length as the image is virtual, so I'm going to keep f positive by reversing the sign in the formula: And therefore Differentiating with respect to t : where vi and vo are the velocities. From the original formula : Substituting for di When do is zero the speeds are the same. As do tends to infinity vi tends to zero. This graph shows vi (x) with f = 10 and vo = 1 So, to answer the original question: As the object approaches the mirror the image accelerates from zero (starting at the focus and travelling 'towards the mirror' albeit virtually), to a maximum when the object hits the mirror. Only at this moment are the two speeds equal (but opposite in sign of course!). Bob You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #6 20131203 12:20:59
Re: Convex Mirror
I do not think so. 'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.' 'God exists because Mathematics is consistent, and the devil exists because we cannot prove it' 'Who are you to judge everything?' Alokananda #7 20131203 18:50:33
Re: Convex Mirrorhi Agnishom,
So they have a different convention. You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #8 20131204 04:10:09
Re: Convex MirrorOk thanks 'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.' 'God exists because Mathematics is consistent, and the devil exists because we cannot prove it' 'Who are you to judge everything?' Alokananda 