A toy rocket engine is securely fastened to a large puck that can glide with neg

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 3.40. kg puck has a velocity of 5.00 i m/s at one instant. Eight seconds later, its velocity is(6i + 16j)m/s. Assuming the rocket engine exerts a constant horizontal force, find the components of the force.(.125 we know the change in velocity during an 8 second time interval. How do you calculate this acceleration? icirc + 2 This is the Y-component of the acceleration; not the force. j)N Find the magnitude ___________ N

Explanation / Answer

You need the x-direction ("i-hat") velocity to change 4 m/s in 8 seconds; that's an acceleration of
ax = (6 - 5)m/s / 6s = 0.1667 m/s
and you need the y ("j-hat") velocity to change by 16 m/s in 6 seconds:
ay = 16m/s / 6s = 2.667 m/s

Multiply the acceleration components by the mass to get the force components:
Fx = 3.4kg * 0.1667m/s = .567 N
Fy = 3.40kg * 2.667m/s = 9.0678 N

This can be written
F = .567N i-hat + 9.0678 j-hat answer
although that arrow should be on top of the F, not beside it.

The magnitude of F can be calculated using Pythagoras:
|F| = (Fx² + Fy²) = 9.0855 N

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