A man walks for 1 minute at a speed of `1 ms^(–1)` and then runs for 1 minute at a speed of `3 ms^(–1)` along a straight track. What is the average speed of the man?

Explanation

This can be maximizing x varying `theta` on ground.

By `y=x tan theta -(gx^(2)(1+tan^(2) theta))/(2u^(2))`
`-25=x tan theta-(10x^(2)(1+tan^(2) theta))/(2xx400)`
`tan^(2)theta(x^(2))-tan(80x)+(x^(2)-2000)=0`
It is quadratic in `tan theta` & for `tan theta` to be real
`6400x^(2)-4x^(2)(x^(2)-2000) gt 0`
`x_("max")=60 m`