Please see question and diagram attached. Please check all steps and unit conver

Question

Please see question and diagram attached. Please check all steps and unit conversions, and show all work. Thank you! A mass of 8 kg is resting on a horizontal, frictionless surface Force 1 is applied to it at 40 degrees below the horizontal in the -x direction, force 2 has a magnitude of 23 N and is applied in the +x direction , and force 3 has a magnitude of 52 N and is applied vertically upwards. When these forces are applied, the normal force acting on the mass is one half the amount of its weight. Also, when these forces are applied, the object moves 6 meters in the +x direction before it is launched horizontally off a cliff which is 23 meters above the ground. How far does the object travel horizontally in the air, in meters, when it hits the ground? Note: in midair, the only force acting on it is gravity Diagrams 4 (page 3 of 6) Fs Fi

Explanation / Answer

As the block will not move vertically

Fy=0

F3 - W + N - F1sin40 = 0

52 - 8x 9.8 +4x9.8 - F1sin40 = 0 .... because N = 1/2 W

F1 = 19.91N

Fx = ma

F2 - F1cos40 = ma

23 - 19.91cos40 = 8a

a = 0.97 m/s^2

V^2 = u^2 + 2as

V^2 = 0 + 2 x 0.97 x 6

V = 3.41 m/s

Finally using projectile motion

U = 3.41 ; = 0 ; x = ? ; y = -23m ; a = - g = -9.8 m/s2

y = xtan - gx2/2Vx2

-23 = 0 - 9.8 x2/ 2x3.41^2

solving for x

x = 7.39 m

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