How Does Projectile Angle Affect Range in Physics?

Click For Summary
Galileo's principle states that projectiles launched at angles equidistant from 45 degrees will have equal ranges when air resistance is ignored. The discussion seeks to prove this by setting the angle of projection as θ = 45 ± ∂ and deriving the range formula R = [(v0^2)*sin(90-2∂)]/g. The transformation to R = [v0^2*cos(±2∂)]/g utilizes the identity cos(2∂) = cos(-2∂). The conclusion drawn is that R(45+θ) equals R(45-θ), indicating symmetry in projectile motion. To fully understand the derivation, the range formula based on initial velocity and angle must be established.
Questions999
Messages
151
Reaction score
0
Galileo showed that, if air resistance is neglected, the ranges for projectiles whose angles of projection exceed or
fall short of 45 degree by the same amount are equal. Prove Galileo’s result.
Answer in my textbook : set θ=45+ - ∂ (I understand this)
Now comes the weird part R = [(v0^2)*sin(90-2∂ ]/g=[V0^2*cos(+-2∂ )]/g.. What formula is this,and how is it transformed this way?

since cos2∂ =cos(-2∂ )
Now we have R(45+θ)=R(45-θ) ..how about this one?How did we get these?
 
Physics news on Phys.org
You need the formula for range given the magnitude of initial velocity and its angle with the horizontal. Do you have it? If not, you will have to derive it from other equations that you have.
 
I have them but I don't know how to relate them :(
 
What equations do you have?
 

Thread 'Magnitude of buoyant force in fluids of different densities'

The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?
View full post »

Similar threads

I need opinions on a Projectile Motion problem that I made up
  • · Replies 11 ·
Replies
11
Views
2K
Projectiles launched at complementary angles
  • · Replies 16 ·
Replies
16
Views
5K
Projectile Motion Max Height and Range
  • · Replies 1 ·
Replies
1
Views
3K
Projectile motion of two balls off a cliff
  • · Replies 4 ·
Replies
4
Views
991
Optimal Angle and Horizontal Range of a Bottle Rocket Projectile
  • · Replies 1 ·
Replies
1
Views
3K
Relationship between Launch height and range of a projectile
  • · Replies 15 ·
Replies
15
Views
26K
How Does Projectile Angle Affect Asymptotic Behavior in Physics Graphs?
  • · Replies 23 ·
Replies
23
Views
3K
Launching a Projectile with Air Resistance
  • · Replies 13 ·
Replies
13
Views
3K
Maximum range on ground for an elevated cannon
  • · Replies 21 ·
Replies
21
Views
4K
How Do You Calculate Minimum and Maximum Velocities in Projectile Motion?
  • · Replies 7 ·
Replies
7
Views
3K