Two ice skaters, Daniel (mass 69 2 kg) and Rebecca (mass 50.8 kg) are practicing

Question

Two ice skaters, Daniel (mass 69 2 kg) and Rebecca (mass 50.8 kg) are practicing. Daniel stops to tie his shoelace and, while at rest, is struck by Rebecca, who is moving at 13 2 m/s before she collides with him After the collision, Rebecca has a velocity of magnitude 6.3 m/s at an angle of 53.7 degree from her initial direction. Both skaters move on the frictionless, horizontal surface of the rink. What are the magnitude and direction of Daniel's velocity after the collision? What is the change in total kinetic energy of the two skaters as a result of the collision?

Explanation / Answer

here,

mass of Daniel , m1 = 69.2 kg

mass of Rebecca , m2 = 50.8 kg

initial speed of Rebecca , u2 = 13.2 m/s

final speed of Rebecca , v2 = 6.3 * ( cos(53.7) i + sin(53.7) j)

v2 = 3.73 m/s i + 5.08 m/s j

a)

let the final speed of Daniel be v1

using conservation of momentum

m1 * u1 + m2 * u2 = m1 * v1 + m2 * v2

50.8 * 13.2 i = 69.2 * v1 + 50.8 * ( 3.73 i + 5.08 j )

v1 = (6.95 i - 3.73 j) m/s

|v1| = sqrt(6.95^2 + 3.73^2) = 7.89 m/s

phi = arctan(3.73/6.95) = 28.2 degree

the final speed of Daniel is 7.89 m/s and 28.2 degree below the initial direction

b)

the change in total kinetic energy , KE = 0.5 * m2 * u2^2 - 0.5 * m1*v1^2 + 0.5 * m2 * v2^2

KE = 0.5 * ( 50.8 * 13.2^2 - 69.2 * 6.3^2 - 50.8 * 7.89^2)

KE = 1471.2 J

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.