Thanks for making me remember why I majored math and calculus with fun problems like these after finishing my exams. Here's hoping for a good thesis in a few.
Personally, i would calculate directly the derivative of x as t/√(100+t^2) where, using the assumption of a costant rate of y, i changed y itself with t (time in minutes). At the end, you just need to set this term equal to 0.5 and solve the equation. Nice video btw. Keep it up.
If we take the vertical position of the red car as a, then we get x^2=10^2+a^2. Doing implicit differentiation, we can find that 2x*(dx/dt)=2a*(da/dt). We know da/dt=1, and we want dx/dt=0.5, so we can just plug those into the equation, and find that 2x*0.5=2a*1, or that x=2a. Substituting 2a in for x gives us (2a)^2=10^2+a^2, or 4a^2=100+a^2. A little bit of algebraic manipulation later, and we see that a^2=100/3, or a=10/sqrt(3). Plugging this back into x=2a tells us that x=20/sqrt(3) when dx/dt=0.5
I challenge u to solve this integral. (sin²x+sinx)/(1+sinx+cosx) Without converting into tan(x/2) because it will become way too long and we were only given 4mins to solve it
