An air pump does 5,600 J of work to launch a water bottle rocket into the air. If the air pump applies 150 N of force to the roc
2 answers:
Answer: 53 m
Explanation:
Work = Force × Displacement
W= F s cosΘ
Where, s is the displacement and F is the force. Θ is the angle between force and displacement
F cosθ is the component of force acting in the horizontal direction.
The air pump applies F = 150 N force at an angle Θ = 45°
W = 5600 J
⇒s = W/F cosθ
Thus, the horizontal distance the water bottle rocket travels is 53 m
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One of the essential concepts to solve this problem is the utilization of the equations of centripetal and gravitational force.
From them it will be possible to find the speed of the body with which the estimated time can be calculated through the kinematic equations of motion. At the same time for the calculation of this speed it is necessary to clarify that this will remain twice the ship, because as we know by relativity, when moving in the same magnitude but in the opposite direction, with respect to the ship the debris will be double speed.
By equilibrium the centrifugal force and the gravitational force are equal therefore
Where
m = mass spacecraft
v = velocity
G = Gravitational Universal Constant
M = Mass of earth
Radius of earth and orbit
Re-arrange to find the velocity
Replacing with our values we have
From the cinematic equations of motion we have to
Remember that the speed is double for the counter-direction of the trajectories.
Replacing
Therefore the time required is 3.778s