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a projectile is projected at an angle of 30° from a building of height 10m with velocity 10m/s, with what velocity it strikes the ground and at what angle

a projectile is projected at an angle of 30° from a building of height 10m with velocity 10m/s, with what velocity it strikes the ground and at what angle

Grade:11

2 Answers

Sam
52 Points
6 years ago
 
in y axis displacement is -10m (taking -y axis as negative)
then s = ut + at2/2
-10 = (10sin30)t  -  10t2/2                     (as velocity in yaxis is 10sin30=5   and  a =  -g as gravity is acting downward)
-10 = 5t – 5t2
5t2 –  5t –  10 = 0
t2 – t – 2 = 0
(t – 2)(t + 1) = 0
so possible value of t will be 2 and -1 sec , as time cannot be negative so t=2sec
so velocity in y axis  Vy = Uy – gt =  10sin30 – 10(2)  =   5 – 20 =  -15m/s
and velocity in x axis Vx = UX = ucos30 =  10 (\sqrt{3})/2 = 5(\sqrt{3}) m/s
 
velocity when strike V = 5\sqrt{3} i  –  5 j
let x be the angle made by velocity with ground
then tan x = 5 / 5\sqrt{3} =  1/\sqrt{3}                =>   x = 30 degree
Jivesh garg
22 Points
6 years ago
You did a mistake in the last steps. Otherwise it`s correct. It`s -15j not -5j. Check it. The answer is 60° 10√3

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