Question

A quidditch match is going on between Hufflepuff and Ravenclaw. A Hufflepuff chaser is flying 10 degrees north of east at a speed of 5 m/s. A bludger is heading east at a speed of 10 m/s. The bludger has a mass of 10 kg, and the player plus broom has a total mass of 80 kg. If the chaser catches the bludger (i.e. they collide and stick together), at what angle north of east do they move? Give both the expression and the numerical answer. (If you are not familiar with Harry Potter and its wizard jargon, you can reframe the question with the Hufflepuff chaser (player) as a soccer player and the bludger as a soccer ball.).

Please every step of the expression

Answer 1

It's an inelastic collision problem ,where final velocity V = m1u1 + m2u2 /(m1+m2)

Where m1 is mass and u1 is velocity of one object , m2 is mass and u2 is velocity of another object . This relation comes from momentum conservation of system.

Here mass of player m1 is 80 kg and velocity u1 is 5 m/s 10 degree north of east.

And mass of bludger m2 is 10 kg and velocity u2 is 10 m/s east direction.

Hence the final velocity V = (( 80kg × (5m/s cos10° East + 5m/s sin 10° North)) + ( 10kg × 10 m/s East)) / (80 kg + 10 kg)

As cos 10° = 0.9848 and sin 10° = 0.1736 ,now put these values on above expression on V ,we get

V = ((400×0.9848 East) + (400×0.1736 North))kg.m/s / 90 kg

V = (393.92 East + 60.44 North) m/s / 90

V = (4.3768 East + 0.6715 North) m/s

And the direction of velocity would be, theeta in radian = tan ^ -1 ( V North component / V East component )

= tan ^-1 ( 0.6715 / 4.3768) = tan ^-1 (0.153422) = 0.152235

Hence theeta in degree would be = 0.152235 × 57.296°= 8.7224°

So , finally they move 8.7224° North of east after collision.