I need help getting to the correct answers Two blocks of clay slide over a level

Question

I need help getting to the correct answers

Two blocks of clay slide over a level, frictionless plane. Block A has a mass of 5.00 kg and slides due east at an initial speed of 10.0 m/s. Block B has a mass of 1.5 kg and slides in a direction 30.0 degrees west of due north at an initial speed of 20.0 m/s. They collide and stick together. (a) Calculate the final speed of the resulting blob. (b) Calculate the direction of motion of the final blob as an angle north of due east. (Answers: 6.70 m/s, 36.6 degrees)

Explanation / Answer

a)

here ,

let the final speed is v

Using conservation of momentum ,

v*(5 + 1.5) = 5 * 10 i + 1.5 *20(-sin(30) i+ j*cos(30))

v *6.5 = 35 i + j 26

v = 5.38 i + 4 j

final speed = sqrt(5.38^2 + 4^2)

final speed = 6.71 m/s

b)

theta = arcctan(4/5.38)

theta = 36.6 degree

the angle is 36.6 degree

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