# Isaac Physics - Maximum Angle Throw

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#1
Hiya! I have been attempting a level 5 kinematics problem but don't seem to be getting anywhere.

A ball is thrown at speed v from the origin

What is the minimum angle to the vertical at which the ball can be thrown so that its distance to the origin is always increasing (i.e. the distance d is always increasing with time)? Give your answer to 3 significant figures.

https://isaacphysics.org/questions/b...2020_21_week12

I have the formulas for both the x and y direction of the distance from the origin. With pythagoras I can find d with these two formulas. I tried to use the discriminant: t(t^2*g^2-3v*cos(theta)*g*t+2v^2) and set it to zero but I can't get theta because I don't have any values for the velocity or time...

I would be grateful for any help.
0
11 months ago
#2
Have a look at HINT 4
It solves it for you
the gradient function has to be greater than zero for all times t
The only way this can happen is for the discriminant of the quadratic equation in t must be greater than ZERO
This will produce an inequality expression in Cos (Theta) hence get minimum angle
You dont need to know the speed at all
1
#3
(Original post by swinroy)
Have a look at HINT 4
It solves it for you
the gradient function has to be greater than zero for all times t
The only way this can happen is for the discriminant of the quadratic equation in t must be greater than ZERO
This will produce an inequality expression in Cos (Theta) hence get minimum angle
You dont need to know the speed at all
Oh thank you so much! I forgot to use the discriminant
0
11 months ago
#4
(Original post by fastnfuriouseng)
Oh thank you so much! I forgot to use the discriminant
Please hit the thumbs up button to give credit
Cheers
1
1 month ago
#5
(Original post by swinroy)
Have a look at HINT 4
It solves it for you
the gradient function has to be greater than zero for all times t
The only way this can happen is for the discriminant of the quadratic equation in t must be greater than ZERO
This will produce an inequality expression in Cos (Theta) hence get minimum angle
You dont need to know the speed at all
Sorry i am doing the same question now, and i am so confused why the discriminant of the gradient function has to be greater than 0. Surely if the gradient function is always greater than 0, then the curve never intersects the axis, so the discriminant is always less than 0?
0
1 month ago
#6
(Original post by YGSK)
Sorry i am doing the same question now, and i am so confused why the discriminant of the gradient function has to be greater than 0. Surely if the gradient function is always greater than 0, then the curve never intersects the axis, so the discriminant is always less than 0?
The minimum value will occur when the discrimiant = 0, but as you say, you want the gradient to be positive, so the quadratic must be positive so the discriminant is < 0.

As a thought experiment, take theta=0, so cos(theta)=1 and the discriminat is 9-8. > 0 This scenario obviously does not have the distance always increasing as it goes straight up, then the distance is decreasing when it comes down.
Last edited by mqb2766; 1 month ago
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