- #1
clarineterr
- 14
- 0
A projectile is fired at a speed v0 from and angle [tex]\theta[/tex] above the horizontal. It has a maximum height H and a range R (on level ground)
Find:
The angle [tex]\theta [/tex] above the horizontal in terms of H and R
The initial speed in terms of H, R and g
and the time of the projectile in terms of H and g.
Relevant Equations:
Hmax= [tex]\frac{\left(v0sin\theta\right)^{2}}{2g}[/tex]
R = [tex]\frac{v0^{2}sin2\theta}{g}[/tex]
Attempt at a solution:
From the maximum height equation: v0sin[tex]\theta[/tex]=[tex]\sqrt{2gh}[/tex]
and from the Range equation: v0cos[tex]\theta[/tex]= [tex]\frac{gR}{2v0sin\theta}[/tex]
then we have v0cos[tex]\theta[/tex]= [tex]\frac{gR}{\sqrt{2gH}}[/tex]
Then tan[tex]\theta[/tex]= [tex]\frac{v0sin\theta}{v0cos\theta}[/tex] = [tex]\frac{2H}{R}[/tex]
so then [tex]\theta[/tex] = tan[tex]^{-1}[/tex][tex]\frac{2H}{R}[/tex]
Then for the second question, I have v0 = [tex]\sqrt{\frac{gR}{sin2\theta}}[/tex]
Then I don't know how to convert it to just be in terms of g, H and R
For the third question I am getting: t = [tex]\frac{2vosin\theta}{g}[/tex]
Find:
The angle [tex]\theta [/tex] above the horizontal in terms of H and R
The initial speed in terms of H, R and g
and the time of the projectile in terms of H and g.
Relevant Equations:
Hmax= [tex]\frac{\left(v0sin\theta\right)^{2}}{2g}[/tex]
R = [tex]\frac{v0^{2}sin2\theta}{g}[/tex]
Attempt at a solution:
From the maximum height equation: v0sin[tex]\theta[/tex]=[tex]\sqrt{2gh}[/tex]
and from the Range equation: v0cos[tex]\theta[/tex]= [tex]\frac{gR}{2v0sin\theta}[/tex]
then we have v0cos[tex]\theta[/tex]= [tex]\frac{gR}{\sqrt{2gH}}[/tex]
Then tan[tex]\theta[/tex]= [tex]\frac{v0sin\theta}{v0cos\theta}[/tex] = [tex]\frac{2H}{R}[/tex]
so then [tex]\theta[/tex] = tan[tex]^{-1}[/tex][tex]\frac{2H}{R}[/tex]
Then for the second question, I have v0 = [tex]\sqrt{\frac{gR}{sin2\theta}}[/tex]
Then I don't know how to convert it to just be in terms of g, H and R
For the third question I am getting: t = [tex]\frac{2vosin\theta}{g}[/tex]