(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

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 7.80-kg puck has a velocity of 4.00 i m/s at one instant. Eight seconds later, its velocity is (6 i + 19 j) m/s. (a) Assuming the rocket engine exerts a constant horizontal force, find the components of the force. (b) Find its magnitude

Explanation / Answer

a)

To find the force, we need to find the acceleration first.
Acceleration along i is (6-4)/8 = 0.25 m/s^2. Acceleration along j is (19-0)/8 = 2.375 m/s^2.
Use the equation F = ma. Because both m and a are known now, simply plug in the values.
Along i: F = (7.8)(0.25) = 1.95 N
Along j: F = (7.8)(2.375) = 18.525 N
So the force is (1.95i + 18.525j) N

b)

To find the magnitude, use the Pythagorean Theorem:
F = ?((Fi)2 + (Fj)2) = ?(3.8025 + 343.176) ? 18.63 N

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