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Grade 11Mechanics

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 does it strike the ground.(take g=10m/s).

Jivesh garg

8 Years agoGrade 11

1 Answer

Sam

8 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 V_y = U_y – gt = 10sin30 – 10(2) = 5 – 20 = -15m/s

and velocity in x axis V_x= U_X = 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

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