Post by Mocha on Feb 19, 2018 14:04:05 GMT
This puzzle is modified from one I read a few weeks ago. Hopefully it will make you think, and not just about math!
A two cars are driving down a straight road, parallel, in the same direction. The cars are identical.
One car is travelling at 70 mi/h, the other is travelling 80 mi/h.
Once the faster car overtakes the smaller car, they both simultaneously notice a fallen tree blocking the road.
(ie. they are both the same distance from the tree)
They both immediately begin to brake.
The slower car barely stopped a hair's width away from the tree.
However, logically, that means the faster car hit the tree.
How fast did the faster car hit the tree?
Bonus Question 1:
At what speed would the fast car have to be travelling for the impact speed to be 20 mi/h?
Bonus Question 2:
The same scenario as the original, but instead of 70 mi/h, x mi/h, and instead of 80 mi/h, (x+10) mi/h.
All three problems are solveable, either with calculus alone, or with algebra + physics. There is no tricky wording, but if you don't think carefully, you'll derive the trick answer instead of the correct one. As a super bonus for those who can solve it both ways, prove the formula you learned in physics to be true using calculus!
A two cars are driving down a straight road, parallel, in the same direction. The cars are identical.
One car is travelling at 70 mi/h, the other is travelling 80 mi/h.
Once the faster car overtakes the smaller car, they both simultaneously notice a fallen tree blocking the road.
(ie. they are both the same distance from the tree)
They both immediately begin to brake.
The slower car barely stopped a hair's width away from the tree.
However, logically, that means the faster car hit the tree.
How fast did the faster car hit the tree?
Bonus Question 1:
At what speed would the fast car have to be travelling for the impact speed to be 20 mi/h?
Bonus Question 2:
The same scenario as the original, but instead of 70 mi/h, x mi/h, and instead of 80 mi/h, (x+10) mi/h.
All three problems are solveable, either with calculus alone, or with algebra + physics. There is no tricky wording, but if you don't think carefully, you'll derive the trick answer instead of the correct one. As a super bonus for those who can solve it both ways, prove the formula you learned in physics to be true using calculus!
