Please show full detail of work for this problem, I got 6.25 degrees, but I am n

Question

Please show full detail of work for this problem, I got 6.25 degrees, but I am not sure if it is correct.

Two people are sliding on a sheet of ice, initially heading at 45o angles relative to the x-axis as shown. When the two people collide, they grab and hold onto each other.

Their masses and velocities before the collision are: M1 = 67 kg, V1 = 1.6 m/s, M2 = 62 kg, V2 = 0.8 m/s.

What is the direction the two people are moving immediately after they collide? Give your answer in degrees from the x-axis, to three digits.

Positive angles are counter-clockwise from the x-axis (above the x-axis) and negative angles are clockwise from the x-axis (below the x-axis).

Please show full detail of work for this problem, I got 6.25 degree s, but I am not sure if it is correct. Two people are sliding on a sheet of ice, initially heading at 45o angles relative to the x-axis as shown. When the two people collide, they grab and hold onto each other. Their masses and velocities before the collision are: M1 = 67 kg, V1 = 1.6 m/s, M2 = 62 kg, V2 = 0.8 m/s. What is the direction the two people are moving immediately after they collide? Give your answer in degree s from the x-axis, to three digits. Positive angles are counter-clockwise from the x-axis (above the x-axis) and negative angles are clockwise from the x-axis (below the x-axis).

Explanation / Answer

When M1 is moving towards the x direction at a 45 degree, M1 has a velocity in the x and y direction.

M1 x direction= sin(45)x1.6m/s=1.13137m/s

M1 y direction= cos(45)x1.6m/s=1.13137m/s

notice that the speed in the x and y direction for M1 is the same. That comes from Trig functions of 45 Degree Angels which cos and the sin are equal

M2 x direction = sin(45)x0.8m/s= .565685m/s

M2 y direction =cos(45)x0.8m/x = -.565685m/s "relize that the magnitude of the velocity for M2 is negative based on the fact that M2 is traveling at an opposite direction in relation to M1.

Velocity for both objects after colliding

x direction

Vsm=[m1V+m2V]/[m1+m2} = .85949 m/s in the x direction

y direction

Vsm=[m1V+m2V]/[m1+m2} = .31573 m/s in the y direction

The direction of the two can be determied by

The angel=inverseTan(sin/cos) = 20.171 degrees

I hope this helps :)

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