Projectile Motion Question

[robbo]

Good Afternoon,
I am stuck on Part c) of this question and I'm not sure where to start.

A man is on top of a building height H above the ground. He is trying to throw a ball through a specific window of another building directly across from him at a distance D away. He throws the ball at a constant speed V. Let the force due to gravity be and the angle of elevation to the horizontal be α.
a) Derive the equations for the horizontal and vertical components of velocity and displacement.

b) Show that the equation of the flight path of the ball is:
[math]y= \frac{-gx^2}{2V^2}(1+tan^2\alpha)+xtan\alpha[/math]
c) Show that if he was to throw the ball directly through the opposite window that the following would be true:
[math]V^4-2gV^2H-g^2D^2 \geq 0[/math]
I assumed I would need to input (D,H) in somewhere but I am unsure where to start.

Thank you!

 

[khansaheb]

Good Afternoon,
I am stuck on Part c) of this question and I'm not sure where to start.

A man is on top of a building height H above the ground. He is trying to throw a ball through a specific window of another building directly across from him at a distance D away. He throws the ball at a constant speed V. Let the force due to gravity be and the angle of elevation to the horizontal be α.
a) Derive the equations for the horizontal and vertical components of velocity and displacement.

b) Show that the equation of the flight path of the ball is:
[math]y= \frac{-gx^2}{2V^2}(1+tan^2\alpha)+xtan\alpha[/math]
c) Show that if he was to throw the ball directly through the opposite window that the following would be true:
[math]V^4-2gV^2H-g^2D^2 \geq 0[/math]
I assumed I would need to input (D,H) in somewhere but I am unsure where to start.

Thank you!

Can you "derive" the equation for the path of a projectile launched from the ground, at an angle "t" ?

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

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Please share your work/thoughts about this problem

 

[robbo]

Yep - Please see below for my answers to part a) and b).

I just have no idea where to start for part c).

 

[Dr.Peterson]

Yep - Please see below for my answers to part a) and b).

I just have no idea where to start for part c).

Imagine you want to find [imath]\alpha[/imath] given that when x=D, y=H. You will have a quadratic equation in [imath]\tan(\alpha)[/imath].

Under what condition can that equation be solved? (Hint: discriminant.)

 

[robbo]

Got it! Good hint with the discriminant.

Thank you!