- #1
Makonia
- 25
- 1
Homework Statement
You are the chief of the Angry Birds (Google it, if you don’t know the reference...it’s not important). You can shoot red birds from a catapult, and they will fly as projectiles under the effect of gravity. Gravity points downwards and has magnitude g = 9.80 m/s2 . Your goal is to hit some nasty green pigs, who have stolen your Angry Bird Eggs. You are able to adjust the angle θ and speed v of the projectile, as it leaves the catapult. The projectile leaves the catapult at a height h above the ground.
a) First, consider the case when a single green pig is placed on the ground, at a distance d from the foot of the catapult. Find a relation between the angle and speed required to hit it. Remember to draw a sketch of the situation.
b) Next consider the case where there are two green pigs. One on the ground at a distance d as before, the other at a distance l < d, and placed on a pole of height h. What should you choose for θ and v in order to hit both pigs 1 with the same red bird? Why must one require l < d? Remember to draw a sketch of the situation.
Homework Equations
This task is related to projectile motion and I'm therefor pretty sure I'm supposed to solve it with the projectile motion equations.
In other words x = Vx(initial)*t because there is no acceleration in the x-axis direction and y = Vy(initial)t - 1/2gt^2
This is by the way a question i got at university but I'm posting it here because the physics seen rather basic, the problem is rather that in task b i need to determine two variabels and I'm not given the distance. My point is that if calculus or som other more advanced methods like advanced algebra could be used to solve this then that should not be a problem for me.
g = gravity = 9.8 m/s^2
d is the distance between 0 and the last pig
θ = is the angle the projectile was shot out with
The Attempt at a Solution
In task a I found an expression for t in x-direction by using the x = Vxt (and setting x to d) and got t = d/Vx
I put this expression for t into the equation in y-dirextion: y = Vyt - 1/2gt^2. By setting y to -h because i think like the projectile is shot from h which is 0 and land on the ground, -h. Also I've used that Vx = Vcosθ an Vy = Vsinθ
I solved this equation for V and as result I got:
V = sqrt((g*d^2)/(2*cos^2(θ)(h+d*tanθ)))
This is the answer I think is correct in task a and I think I might have to use it to solve b but I am not sure.
The b task is difficult because I need to find both θ and the innitial speed in order to hit both pigs an by my logic there is an endles different possible answers to that.
I've been trying to find equations for t or v but I have no idea how to make sure it hits both targets and write an equation on that so if anyone think they can solve it or help me by giving me som hints or pointers to where i should start at least that would be most appreciated. Also sorry for my bad english but I hope you understand