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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 =30√3 m is the horizontal

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 =30√3 m is the horizontal

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Grade:10

2 Answers

Saurabh Koranglekar
askIITians Faculty 10335 Points
4 years ago
Dear student

What is to be found or proven in the question is not mentioned, kindly repost with full question

However, time of flight and horizontal distance are equal

Regards
Khimraj
3007 Points
4 years ago
 
From foot,
let its vel. be u
in x- dircn.
200 = ucos60*t
ut = 400 …......................(1)
in y – direcn.
100 = usin60*t – 0.5gt^2
100 = (root(3)/2)*ut) – 0.5gt^2............................(2)
put ut from (1) in (2)
100 = 200root3 – 0.5gt^2
5t^2 = 200root3 – 100
t^2 = 40root3 – 20
t^2 = 49.2 = 49 (approx.)
t = 7 seconds.
 
u = 400/7 = 57.14 m/s
 
From top of cliff,
let h be the height of the cliff and this h (let) is less than 100m.
then 
 
in x – direcn.
200 = v*cos30*7 (time = same as simult. shot)
v = (400/7)*root3
v = 98.85 m/s
 
in y – direcn.
 (100 – h) = vsin30 – 0.5g*49
h = 100 – 98.85/2 – 245
h = -194.425 m
 
here h comes negative it means h is greater than 100 m where the object is located.
 

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