Here, we will use the relation between the horizontal range R, acceleration due to gravity g, initial speed u and the maximum height H, which is given as:
R = H ⇒u2sin2θ/g = 2× u2sin2θ/g
⇒ 2sinθcosθ = sin2θ
⇒ tanθ = 2
From this we get the following values:
sinθ =2√5
cosθ = 1√5
Now, by substituting these values to find the horizontal range R:
R = u2×2 sinθ cos θg
⇒ R = u2 × 2 × 2/√×1/√5g
∴R = 4u2/5g
Therefore, we get the required horizontal range R of the object, projected from the ground with speed u.
Tags:
Physics