To model a spacecraft, a toy rocket engine is securely fastened to a large puck, which can glide with negligible friction over a horizontal surface, taken as the xy plane. The 4.00-kg puck has a velocity of 300ˆi m/s at one instant. Eight seconds later, its velocity is to be (800ˆi $ 10.0ˆj) m/s. Assuming the rocket engine exerts a constant horizontal force, find (a) the components of the force and (b) its magnitude.
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a) mass puck = 3.20 kg
v = 2.00 m/s at one instant
t = 8 s
vf = (6i+19j)m/s
acceleration = velocity/time
= [(6i+19j)m/s - (2.00i)m/s]/8s
= [(4i+19j)m/s]/8s
= (0.5i+ 2.375j)m/s²
b) F = (mass)(acceleration)
= (3.20kg)(0.5i+2.375j)m/s²
= (1.6i + 7.6j) N
| f | = F = [Fx² + Fy²] ^(1/2) <----- (square root)
= [(1.6N)²+(7.6N)²] ^(1/2)
= 7.77 N
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