Air hockey si a game playedon a table. A puck slides freely on a cushion of air.

Question

Air hockey si a game playedon a table. A puck slides freely on a cushion of air. opposing players strike the puck with a hand held round paddle. in one case while playing air hockey the puck comes towards you with a speed of 0.8 m/s at an angle of 30 above the x-axis in the xz plane. You strike it with your paddle, and after the collision, the puck travels in the +x direction with a speed of 1.9 m/s toward the opponment's goal. The mass of the puck is 0.02 kg

Calculate the net impulse on the puck during the collision with the paddle. Answer in vector form

my work:

u = -.8 cos(30) + .8 sin(30)

m = .02 kg

v = 1.9

.02(1.9 + .693 -.4)

.02( 2.593 - .4)

(0.05186 - .008)

sqrt(0.05186^2 + .008^2) = 0.05247

So in vector form I know the answer is (0.05247, 0, __)

What is the z part? because its not 0 or 0.05247

Answer 1

Δp_x = m(v_x^'-v_x) = (.02kg)(1.9 + .8cos(30) m/s) = .051856 kgm/s (The apostrophe indicates after hit)

Δp_z = m(-v_z) = .02kg(-.8sin(30)) = -.008 kgm/s (This is the z part. If this doesn't work, try +)

The problem doesn't make the sign of z clear. I'm assuming it had a +z component originally.

.05247 is the total impulse, not the impulse broken into parts. The answer to the impulse components are the values above. You should write your <i,k> vector with a comma between the x and z components so it doesn't look like you're adding the x and z components algebraically. Your answer is written above sqrt() line.

Please consider a tutor. Take care.