An object is falling from a height of 7.5 meters. At what height will its velocity be 7 meters/second?
1 answer:
Answer:
5.0 m
Explanation:
The velocity of the object at time t is given by
where a=9.8 m/s^2 is the acceleration of gravity and t is the time. If we substitute v=7 m/s, we can find the time t at which the velocity became 7 m/s:
The height of the object at time t, h(t), is given by the equation
where is the initial height. By substituting t=0.71 s inside the equation, we find the height h(t) at which the velocity is 7 m/s:
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Answer:
8.97 Watt
Explanation:
Resistance, R = 20 ohm
Inductance, L = 10 mH
V(t) = 20 Cos (1000 t + 45°)
Compare with the standard equation
V(t) = Vo Cos(ωt + Ф)
Ф = 45°
ω = 1000 rad/s
Vo = 20 V
Inductive reactance, XL = ωL = 1000 x 0.01 = 10 ohm
impedance is Z.
Z = 22.36 ohm
Apparent power is given by
P = Vrms x Irms
P = 14.144 x 0.634
P = 8.97 Watt
1) Initial upward acceleration:
2) Mass of burned fuel:
Explanation:
1)
There are two forces acting on the rocket at the beginning:
- The force of gravity, of magnitude , in the downward direction, where
is the rocket's mass
is the acceleration of gravity
- The thrust of the motor, T, in the upward direction, of magnitude
According to Newton's second law of motion, the net force on the rocket must be equal to the product between its mass and its acceleration, so we can write:
(1)
where a is the acceleration of the rocket.
Solving for a, we find the initial acceleration:
2)
When the rocket reaches an altitude of 5000 m, its acceleration has increased to
The reason for this increase is that the mass of the rocket has decreased, because the rocket has burned some fuel.
We can therefore rewrite eq.(1) as
where
is the new mass of the rocket
Re-arranging the equation and solving for m', we find
And since the initial mass of the rocket was
This means that the mass of fuel burned is