Question

Two ice skaters, with masses of 69 kg and 57 kg , stand facing each other on a 18-m-wide frozen river. The skaters push off against each other, glide backward straight toward the river's edges, and reach the edges at exactly the same time. how far did the 73kg skater glide?

Answer 1

Answer:

The 69 kg skater travels a distance of 8.14 m and the 57 kg skater travels a distance of 9.857 m

Explanation:

Assume both skaters are at rest before the push, so their velocities and their total momentum must be 0. According to the law of momentum conservation, their momentum after the push must also be 0 too.

$m_1v_1 - m_2v_2 = 0$

where m1, v1 are the mass and velocity of the 69kg skater.

           m2, v2 are the mass and velocity of the 57kg skater. v2 is negative because it's in opposite direction with respect to v1

$69v_1 - 57v_2 = 0$

$69v_1 = 57v_2$

$v_1 = v_2\frac{57}{69} = 0.826v_2$

Since both skaters reaches the edges at the same time, suppose their speeds are constant, they must have traveled a total distance of 18m within the same time t

$s_1 + s_2 = s$

where $s_1 = v_1t, s_2 = v_2t$, s = 18 are the distances traveled by the 69kg skater, the 57kg skater and the total distance traveled, respectively.

$v_1t + v_2t = 18$

$t(v_1 + v_2) = 18$

we can substitute $v_1 = 0.826v_2$

$t(0.826v_2 + v_2) = 18$

$1.826tv_2 = 18$

$tv_2 = 18/1.826 = 9.857$

$s_2 = 9.857m$

$s_1 = s - s_2 = 18 - 9.857 = 8.143 m$

So the 69 kg skater travels a distance of 8.14 m and the 57 kg skater travels a distance of 9.857 m