(a) Assuming the rocket engine exerts a constant horizontal force, find the comp

Question

(a) Assuming the rocket engine exerts a constant horizontal force, find the components of the force.

(b) Find its magnitude.

_____ N

A toy rocket engine is securely fastened to a large puck that can glide with negligible friction over a horizontal surface, taken as the xy plane. The 6.20-kg puck has a velocity of 2.00 j hat ) (b) Find its magnitude. _____ N What + _________ j hat) m/s. (a) Assuming the rocket engine exerts a constant horizontal force, find the components of the force. ( _______ i hat + 12 i hat m/s at one instant. Eight seconds later, its velocity is (6

Explanation / Answer

v(0) = 2.00 i + 0j

v(8) = 6.00i + 12.0 j

r = xi + yj

dr/dt = dx/dt i + dy/dt j

F = ma
F = constant

F = mdv/dt
Fdt = mdv

taking integral of both sides

F*t = mv + c

F*0 = 6.2*(2.0i) + c

F*8 = 6.2*(6.00i + 12.0j) + c

solve for c on one equation and put in the second equation

0 = +12.4i + 8F -37.2.i - 74.4 j
0 = -24.8 i + 8F - 74.4 j

then solve for F

F = 24.8/8 i + (74.4/8 )j
F = 3.1 i + 9.3j

to check

a = F/m

a = (3.1i + 9.3j)/6.2
a = 0.5i + 1.5j
dv/dt = a

dv = adt
v = at + c
v(0) = 0 + c = 2.00 i
c = 3.00 i

v(8) = 8(0.5i + 1.5j) + 2.00 i
v(8) = 4.0i + 12.0j + 2.00 i
v(8) = 6.0i + 12.0j

I hope that helped its got alot of calculus

2) F = 3.1i + 9.3j

magnitude of F = sqrt( 3.1^2 + 9.3^2) = sqrt(175.863)

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