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Grade 11Mechanics

Shots fired simultaneously from the top and foot of a vertical cliff at elevation of 30 degree and 60 degree respectively, strike an object simultaneously which is at height of 100 m. from the ground and at a horizontal distance of 200m. from the cliff. Find the height of the cliff. Find the height of the cliff, the velocities of projection of the shots and the time taken by the shots to hit the object.(g=10m/sec.)How to solve dis question?

Profile image of adi
10 Years agoGrade 11
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1 Answer

Profile image of Vikas TU
10 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.