Betty Bodycheck (mB = 55 kg, vB = 22.0 km/h in the positive x-direction) and Sally Slasher (mS = 45 kg, vS = 28.0 km/h in the positive y-direction) are both racing to get to a hockey puck. Immediately after the collision, Betty is heading in a direction that is 76.0° counterclockwise from her original direction, and Sally is heading back and to her right in a direction that is 12.0° from the x-axis.
What are Betty and Sally's final kinetic energies?
I got these:
V Betty = 5.51 m/s
V Sally = 5 . 99 m/s
I used the formula
k = 1/2 * m * v^2
I got these:
K Betty = 834.90 J
K sally = 807 J
I thought that i got the right answer but the book has the answer and it is Betty : 1.55kJ and Sally = 649 J
What is the correct answer?
I need to get the answer of the book
What I need to do?
55*22 = 1210 = 55 Vb cos 76+ 45 Vs cos 12
45*26 = 1260 = 55 Vb sin 76 - 45 Vs sin 12
1210 = 13.3 Vb + 44.0 Vs
1260 = 53.4 Vb - 9.36 Vs times 44/9.36
1210 = 13.3 Vb + 44.0 Vs
5922 = 251 Vb - 44.0 Vs
-------------------------
7132 = 264.3 Vb
Vb = 27 km/hr = 7.5 m/s humm, we disagree
Keb = (1/2)55 (7.5^2) = 1545 J = 1.55kJ
I agree with your book :)
Thanks man, you are awesome
To find the correct answer, let's go over the steps of the problem and recheck the calculations.
First, let's calculate the final velocities of Betty and Sally after the collision.
Given:
mBetty = 55 kg
vBetty = 22.0 km/h = 22.0 * (1000/3600) m/s (convert km/h to m/s)
mSally = 45 kg
vSally = 28.0 km/h = 28.0 * (1000/3600) m/s (convert km/h to m/s)
We can find the components of their velocities in the x and y directions:
vxBetty = vBetty * cos(76.0°) (since 76.0° counterclockwise from the x-direction)
vyBetty = vBetty * sin(76.0°)
vxSally = vSally * cos(12.0°) (since 12.0° from the x-axis)
vySally = vSally * sin(12.0°)
Next, let's use the law of conservation of momentum to find the final velocities:
Initial momentum in the x direction = Final momentum in the x direction
mBetty * vBetty = mBetty * vxBetty + mSally * vxSally
From this equation, we can solve for vxBetty.
Similarly, the initial momentum in the y direction equals the final momentum in the y direction, so we have:
mBetty * 0 + mSally * vSally = mBetty * vyBetty + mSally * vySally
From this equation, we can solve for vyBetty.
Now that we have the components of Betty's velocity, we can calculate her final overall velocity:
vBetty (final) = sqrt(vxBetty^2 + vyBetty^2)
Finally, we can calculate the final kinetic energy for both Betty and Sally using the formula:
K = 1/2 * m * v^2
where m is the mass and v is the velocity.
With these steps, go ahead and recalculate the final velocities and kinetic energies for Betty and Sally and compare them to the book's answer.