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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 9.00-kg puck has a velocity of 2.00 î m/s at one instant. Eight seconds later, its velocity is (6 î + 16 ĵ) m/s.a) Assuming the rocket engine exerts a constant horizontal force, find the components of the force.b) Find its magnitude.

Question

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 9.00-kg puck has a velocity of 2.00 î m/s at one instant. Eight seconds later, its velocity is (6 î + 16 ĵ) m/s.

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

b) Find its magnitude.

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Step 1

The initial velocity of the puck is 2.00im/s, and the final velocity is (6i+16j)m/s.

(a)Write the expression for the components of velocity.

-6m/s
-1
-2.00m/s
a
t
t-8.00s
6m/s-2m/s
8.00s
0.5m/s
16 m/s
a
8.00s
-2m/s
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Image Transcriptionclose

-6m/s -1 -2.00m/s a t t-8.00s 6m/s-2m/s 8.00s 0.5m/s 16 m/s a 8.00s -2m/s

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Step 2

Write the expression for the horizontal component, and vertical component of velocity.

m -9.00kg
F ma
a =0.5m/s
9.00kg x0.5 m/s
=4.5N
[a,-2 m/s]
F ma
9.00kgx2m/s
-18N
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Image Transcriptionclose

m -9.00kg F ma a =0.5m/s 9.00kg x0.5 m/s =4.5N [a,-2 m/s] F ma 9.00kgx2m/s -18N

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Step 3

Hence the expression for fo...

F = Fi Fi
4.5Ni 18Nj
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Image Transcriptionclose

F = Fi Fi 4.5Ni 18Nj

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