Question

Two ice skaters approach each other at right angles. Skater A has a mass of 54.5 kg and travels in the +x direction at 1.51 m/s. Skater B has a mass of 33.6 kg and is moving in the +y direction at 2.28 m/s. They collide and cling together. Find the final speed of the couple. Answer in units of m/s.\

Answer 1

The final speed of the couple is 2.08 m/s.

Step-by-step explanation:

The final speed of the couple can be found using the principles of conservation of momentum.

When two objects collide and cling together, the total momentum before the collision is equal to the total momentum after the collision.

Using the equation:

m1v1 + m2v2 = (m1 + m2)vf

where m1, v1 are the mass and velocity of Skater A, m2, v2 are the mass and velocity of Skater B, and vf is the final velocity of the couple:

Plugging in the given values:

(54.5 kg)(1.51 m/s) + (33.6 kg)(2.28 m/s) = (54.5 kg + 33.6 kg)vf

vf = (54.5 kg)(1.51 m/s) + (33.6 kg)(2.28 m/s) / (54.5 kg + 33.6 kg)

vf = 2.08 m/s

Answer 2

Answer: 1.27 m/s^2

Step-by-step explanation:

from the question we are given the following

mass of A = 54.5 kg

mass of B = 33.6 kg

mass of A and B = 88.1 kg

velocity of A = 1.51 m/s ( at +x direction )

velocity of B = 2.28 m/s ( at +y direction )

the first diagram below shows the motion of skaters A and B before and after collision

to solve this question we would apply the formula momentum = mass x velocity

momentum of A = 54.5 x 1.51 = 82.3 kgm/s

momentum of B = 33.6 x 2.28 = 76.6 kgm/s

using the momentum obtained above, we rearrange the motion of skaters A and B to form a right angle triangle with the momentum of A on the x axis , momentum of B on the y axis and the unknown momentum of A and B as the hypothenus.

applying Pythagoras theorem momentum of A and B =
`\sqrt{(momentum of A^(2) + momentum of B^(2)  )}`

therefore momentum of A and B =
`\sqrt{82.3^(2) +76.6^(2)  }`

= 112.4 kgm/s

recall that momentum = mass x velocity

therefore velocity = momentum / mass

velocity of A and B = 112.4 / 88.1 = 1.27 m/s^2