Projectiles Question (1 Viewer)

[iStudent]

Just the last part thanks (iii)

 

[QZP]

Hint: Express as a quadratic in tan and then use root-coefficient relationships!

 

[iStudent]

Yup got it

 

[dunjaaa]

Lets assume that there is a point satisfying θ(1) < pi/4, θ(2) < pi/4. Therefore tan[θ(1)] < 1, tan[θ(2)] < 1. Therefore tanθ(1)tanθ(2) < 1 (i.e. product of roots < 1). Hence, (x^2+4hy)/(x^2) < 1 -> x^2+4hy < x^2 (x^2 > 0) -> 4hy < 0 -> y < 0. Contradiction!

 

[iStudent]

Lets assume that there is a point satisfying θ(1) < pi/4, θ(2) < pi/4. Therefore tan[θ(1)] < 1, tan[θ(2)] < 1. Therefore tanθ(1)tanθ(2) < 1 (i.e. product of roots < 1). Hence, (x^2+4hy)/(x^2) < 1 -> x^2+4hy < x^2 (x^2 > 0) -> 4hy < 0 -> y < 0. Contradiction!

What made you think of using product of roots though? (I get why it works, but the hard part is thinking of when to use them)

 

[dunjaaa]

Well, it was intuitive I guess. When you have 2 numbers less than one, then the multiplication of the two numbers must also be less than one. I was also trying to link the quadratic in terms of tan into some form of inequality.