Question

Show that there are two angles of projection for a projectile to have the same range. What will be the maximum height attained in two cases? Compare the heights for theta=30 degree and 60 degree

Answer 1

Answer: Maximum height attained in two case are $\frac{u_{1}^{2}  }{4g}$ and  $\frac{u_{1}^{2}  }{4g}$  respectively.

Explanation: Because of range is same in two cases,we can give $H_{1}$  and $H_{2}$  as attached in the image.

Answer 2

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Let the two angles be  θ  

1

​  

  and  θ  

2

​  

 and the projectile velocity be u

Horizontal range        R=  

g

u  

2

sin(2θ  

1

​  

)

​  

=  

g

u  

2

sin(2θ  

2

​  

)

​  

=  

g

u  

2

sin(180−2θ  

2

​  

)

​  

 

⟹    2θ  

1

​  

=180  

o

−2θ  

2

​  

 

⟹          θ  

2

​  

=90−θ  

1

​  

                       

Maximum height attained              H  

1

​  

=  

2g

u  

2

sin  

2

θ  

1

​  

 

​  

         

Similarly         H  

2

​  

=  

2g

u  

2

sin  

2

θ  

2

​  

 

​  

=  

2g

u  

2

sin  

2

(90−θ  

1

​  

)

​  

=  

2g

u  

2

cos  

2

θ  

1

​  

 

​  

         

 

∴    H=H  

1

​  

+H  

2

​  

=  

2g

u  

2

(sin  

2

θ  

1

​  

+cos  

2

θ  

2

​  

)

​  

=  

2g

u  

2

 

​