Question

For a projectile thrown into space with a speed v, the horizontal range is `(sqrt3"v"^2)/(2"g")`. The vertical range is `"v"^2/(8"g")`. The angle which the projectile makes with the horizontal initially is ______.

Options

• 15°

• 30°

• 45°

• 60°

Answer 1

For a projectile thrown into space with a speed v, the horizontal range is `(sqrt3"v"^2)/(2"g")`. The vertical range is `"v"^2/(8"g")`. The angle which the projectile makes with the horizontal initially is 30°.

Explanation:

`("u"^2sin2theta)/"g" = (sqrt3"v"^2)/(2"g")`

⇒ `sin2theta = sqrt3/2`

⇒ `theta = 30^circ`

`("u"^2sin^2theta)/(2"g") = "u"^2/(8"g")`

⇒ `sintheta = 1/2`

or θ = 30°