Projectile Motion and the Range Formula

AI Thread Summary
The range formula for projectile motion can be simplified using the identity sin(2x) = 2sin(x)cos(x). By applying this identity, the original formula R = 2v^2 sin(theta) cos(theta)/g simplifies to R = v^2 sin(2theta)/g. This derivation is based on the sine addition formula, where setting a = b leads to the simplification. Understanding these trigonometric identities can make calculations easier. The simplified formula is essential for analyzing projectile motion effectively.
tharindu
Messages
4
Reaction score
0
Hey Guys

Im wondering if anyone could help me simplify the range formula for projectile motion. So far I've got R=2v^2 sin(theta) cos(theta)/g.

Help will be appreciated. Thanks
 
Physics news on Phys.org
Have you seen the identity sin(2x)=2sinxcosx?
 
No i havent
 
Using that identity, you can simplify the range formula easily.

Note that the identity can be derived from sin(a+b)=sin(a)cos(b)+sin(b)cos(a). Set a=b and you get sin(2a)=sin(a)cos(a)+sin(a)cos(a)=2sin(a)cos(a)
 
so then the formula simplifies down to
R= v^2 sin(2x)/g ?
 

Thread 'Struggling to understand the concept of this question (ice cube in water optics question)'

TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
View full post »
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
View full post »

Similar threads

Relationship between horizontal range and angle of launch
Replies
7
Views
3K
Find Projectile Flight Time Given Only Maximum Height
Replies
4
Views
2K
Relationship between Launch height and range of a projectile
Replies
15
Views
25K
How Do You Solve a Projectile Motion Problem?
Replies
3
Views
4K
Using conservation of energy and momentum in projectile motion
Replies
18
Views
1K
Projectile motion with (constant) wind velocity
Replies
8
Views
2K
Projectile Motion -- Help please understanding these basic problems
Replies
4
Views
1K
In the horizontal direction, what is the initial velocity of the projectile?
Replies
1
Views
1K
Propagation of Error and Relative Error
Replies
10
Views
2K
2 Projectiles are fired simultaneously
Replies
3
Views
2K

Hot Threads

Recent Insights

Back
Top