Q.372. Projectile Motion.

Question 372.
The ball is thrown off the top of the building. If it strikes the ground at B in 3 s, determine the initial velocity v_a and the inclination angle θ_a at which it was thrown. Also, find the magnitude of the ball's velocity when it strikes  the ground.

Answer 372.
Horizontal and vertical components of the velocity are
v_a cos(θ_a) and v_a sin(θ_a) respectively.

For the horizontal displacement,
v_a cos(θ_a) * 3 = 60
=> v_a cos(θ_a) = 20 ... ( 1 )

For the vertical displacement,
v_a sin(θ_a) * 3 - (1/2) g*(3^2) = - 75
=> v_a sin(θ_a) = 23 ... ( 2 )

Squarring and adding eqns. ( 1 ) and ( 2 ),
v_a^2 = 20^2 + 23^2
=> v_a = 30.5 ft/s

Plugging this value in eqn. ( 1 ),
cos(θ_a) = (20)/(30.5)
=> θ_a = 49°.

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