a toy airplane is flying at a speed of 8 m/s with an acceleration of 0.9 m/s^2. How fast is it flying after 2 seconds?
1 answer:
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a) The launch velocity of the rocket is 5.48 m/s
b) The maximum height is 1.53 m
Explanation:
a)
We can solve this part by applying the law of conservation of energy, by considering the kinetic energy and the elastic potential energy only, since there is no change in gravitational potential energy and no friction is involved.
The total energy when the spring is compressed is:
with
(initial kinetic energy is zero)
is the elastic potential energy stored in the spring, with
k = 450 N/m (spring constant)
x = 0.10 m (compression of the spring)
The total energy when the spring is relased is:
with
(final kinetic energy), with
m = 0.15 kg (mass of the rocket)
v = velocity of launch of the rocket
(elastic potential energy is zero when the spring is released)
Combining the two equations we get
And solving for v,
b)
In this part instead we consider only the kinetic energy and the gravitational potential energy, since the spring is at rest so its energy is now zero.
The total energy at the launch is:
where
(initial kinetic energy), with
m = 0.15 kg (mass of the rocket)
v = 5.48 m/s (velocity of launch of the rocket)
(initial gravitational potential energy is zero)
The total energy at the point of maximum height is:
where
(kinetic energy is zero since speed is zero)
(final gravitational potential energy), with
m = 0.15 kg
(acceleration of gravity)
h = ? (maximum height)
Combining the two equations we find
And solving for h,
Learn more about potential energy and kinetic energy:
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Answer:
F=248.5W N
Explanation:
Newton's 2nd Law tells us that F=ma. We will use their averages always. The average acceleration the tennis ball experimented is, by definition:
Since we start counting at 0s and the ball departs from rest, this is just
So we can write:
Where in the last step we have just multiplied and divided by g, the acceleration of gravity. This allows us to introduce the weight of the ball W since W=gm, so we have:
Substituting our values:
Where the average force exerted has been written it terms of the tennis ball's weight W.