Question

prove that a gun will shoot three times as high when it's angle of elevation is 60°as when it is 30°,but cover the same horizontal range?​

Answer 1

Answer:

“G'day mate,

Explanation:

The horizontal distance is

R=\frac{v^2}{g}\sin(2\alpha)R=

g

v

2

​

sin(2α)

R_1=\frac{v^2}{g}\sin60=\frac{\sqrt{3}v^2}{2g}R

1

​

=

g

v

2

​

sin60=

2g

3

​

v

2

​

R_2=\frac{v^2}{g}\sin120=\frac{\sqrt{3}v^2}{2g}R

2

​

=

g

v

2

​

sin120=

2g

3

​

v

2

​

Thus,

R_1=R_2R

1

​

=R

2

​

h_1=\frac{v^2}{2g}\sin^230=\frac{v^2}{8g}h

1

​

=

2g

v

2

​

sin

2

30=

8g

v

2

​

h_2=\frac{v^2}{2g}\sin^260=\frac{3v^2}{8g}=3h_1h

2

​

=

2g

v

2

​

sin

2

60=

8g

3v

2

​

=3h

1

​