A roller-coaster car has a mass of 494 kg when fully loaded with passThree force

Question

A roller-coaster car has a mass of 494 kg when fully loaded with passThree forces acting on an object are given by vector F1 = ( - 2.20 i hat + 2.10 j ) N, vector F2 = ( 4.80 i hat + 3.00 j) N, and vector F3 = ( 45.5 i hat + 50.0 j) N. The object experiences an acceleration of magnitude 3.55 m/s^2.

(a) What is the direction of the acceleration?______° (from the positive x axis)

(b) What is the mass of the object?_______

(c) If the object is initially at rest, what is its speed after 19.0 s?_______

(d) What are the velocity components of the object after 19.0 s?

(_________ i +___________ j )

Please state the answer, show steps and please double check work. Been getting too many wrong answers. Thank you!

Explanation / Answer

a) direction of the acceleration= arctan(Fy/Fx)= arctan(1.145530145530146)=48.88 degree

b) m=F/a

F=sqrt(Fx^2 +Fy^2)= sqrt(48.1^2 +55.1^2)=sqrt(5349.62)=73.1411 N

a=3.55 m/s^2.

m= 73.1411/3.55= 20.6 kg

c) If the object is initially at rest, its speed after 19.0 s is given as

vf=vi+at = 0+3.55*19=67.45 m/s

d) The x - and y - components of the velocity of the object are determined to be as follows:

sin ( theta ) = y / vf
y = vf * sin ( theta )
y = 67.45 m/s * sin (48.88 degrees )
y = -66.30 m/s
cos ( theta ) = x / vf
x = vf * cos ( theta )
x = 67.45 m/s * cos (48.88 degrees )
x = 12.43 m/s

v=12.43 i+ ( -66.30)j

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