A balloon moves vertically above point A. At height h₁, a girl at point B, distance d from A, sees it at 45° to the vertical. When the balloon rises further by h₂, it is seen at 60° to the vertical after the girl moves a further 2.464d to point C. Given tan30°=0.5774, h₂ is:

Question

G1 Physics · Accepted Answer

At B the line of sight is 45° to vertical, so also 45° to horizontal and h₁=d. At C, distance AC=d+2.464d=3.464d and the line of sight is 60° to vertical, i.e. 30° to horizontal. Hence h₁+h₂=AC tan30°=3.464d×0.5774≈2d. Thus h₂=d. Hence option A.