A dinner plate falls vertically to the floor and breaks up into three pieces, which slide horizontally along the floor. Immediately after the impact, a 320-g piece moves along the x-axis with a speed of 2.00 m/s and a 355-g piece moves along the y-axis with a speed of 1.50 m/s. The third piece has a mass of 100 g. In what direction relative to the + x-axis does the third piece move?

(a) 39.8º from the + x-axis

(b) 36.9° from the + x-axis

(c) 39.9° from the + x-axis

(d) 216.9° from the + x-axis

(e) 219.8° from the + X-axis

Question

Physics

Moore

22 December, 19:57

A dinner plate falls vertically to the floor and breaks up into three pieces, which slide horizontally along the floor. Immediately after the impact, a 320-g piece moves along the x-axis with a speed of 2.00 m/s and a 355-g piece moves along the y-axis with a speed of 1.50 m/s. The third piece has a mass of 100 g. In what direction relative to the + x-axis does the third piece move?

(a) 39.8º from the + x-axis

(b) 36.9° from the + x-axis

(c) 39.9° from the + x-axis

(d) 216.9° from the + x-axis

(e) 219.8° from the + X-axis

+1

Answers (1)

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Bullwinkle · Answer 1

M1 Vx1 + M2 Vx2 + M3 Vx3 = 0 conservation of momentum in x direction

Vx3 = - (M1 Vx1 + M2 Vx2) / M3

Vx3 = - 320 * 2 / 100 = - 6.4 m/s M2 has no x-component of momentum

Likewise:

Vy3 = - (M1 Vy1 + M2 Vy2) / M3

Vy3 = - 355 * 1.5 / 100 = - 5.33 m/s

tan theta = - 5.33 / - 6.4 =.833 where theta is in the third quadrant and measured from the negative x-axis

theta = 39.8 deg

180 + 39.8 = 219.8 from the positive x-axis