Question

Two shots are fired simultaneously from the top and bottom of a vertical cliff with the elevation α = 30°, β = 60°, respectively as in Fig. The shots strike an object simultaneously at the same point. If a =30√3 m is the horizontal distance of the object from the cliff, then the height ℎ:

Answer 1

Answer:

Height of cliff = 60 m

Explanation :

Two shots are fired simultaneously from the top and bottom of a vertical cliff with the elevation α = 30°, β = 60°, respectively as in Fig. The shots strike an object simultaneously at the same point. If a =30√3 m is the horizontal distance of the object from the cliff, then the height ℎ:

Here ignoring the gravity & air resistance

Let say vertical height = x m  from top of the cliff  where the object is striked

Tan θ = Perpendicular / Base

=> Tan α = Vertical Distance above cliff / Horizontal distance from cliff

=> Tan 30° = x/30√3

=> 1/√3 = x/30√3

=> x = 30

Tan β = Vertical Distance from bottom of cliff / Horizontal distance from cliff

Vertical Distance from bottom of cliff = height of cliff + Vertical Distance above cliff

=> Vertical Distance from bottom of cliff  = h + 30 m

=> Tan 60° = (h + 30)/30√3

=> √3 = (h + 30)/30√3

=> 90 = h + 30

=> h = 60

Height of cliff = 60 m