Suppose that 2 J of work is needed to stretch a spring from its natural length of 34 cm to a length of 46 cm. (a) How much work
1 answer:
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Answer:
The ball would have landed 3.31m farther if the downward angle were 6.0° instead.
Explanation:
In order to solve this problem we must first start by doing a drawing that will represent the situation. (See picture attached).
We can see in the picture that the least the angle the farther the ball will go. So we need to find the A and B position to determine how farther the second shot would go. Let's start with point A.
So, first we need to determine the components of the velocity of the ball, like this:
we pick the positive one, so it takes 0.317s for the ball to hit on point A.
so now we can find the distance from the net to point A with this time. We can find it like this:
Once we found the distance between the net and point A, we can similarly find the distance between the net and point B:
t= -0.9159s or t=0.468s
we pick the positive one, so it takes 0.468s for the ball to hit on point B.
so now we can find the distance from the net to point B with this time. We can find it like this:
So once we got the two distances we can now find the difference between them:
so the ball would have landed 3.31m farther if the downward angle were 6.0° instead.
a) The acceleration of gravity is
b) The critical velocity is 6668 m/s (24,006 km/h)
c) The period of the orbit is 8452 s
d) The satellite completes 10.2 orbits per day
e) The escape velocity of the satellite is 9430 m/s
f) The escape velocity of the rocket is 11,191 m/s
Explanation:
a)
The acceleration of gravity for an object near a planet is given by
where
G is the gravitational constant
M is the mass of the planet
R is the radius of the planet
h is the height above the surface
In this problem,
(mass of the Earth)
(Earth's radius)
(altitude of the satellite)
Substituting,
b)
The critical velocity for a satellite orbiting around a planet is given by
where we have again:
(mass of the Earth)
(Earth's radius)
(altitude of the satellite)
Substituting,
Converting into km/h,
c)
The period of the orbit is given by the circumference of the orbit divided by the velocity:
where
v = 6668 m/s
Substituting,
d)
One day consists of:
While the period of the orbit is
T = 8452 s
So, the number of orbits completed by the satellite in one day is
e)
The escape velocity for an object in the gravitational field of a planet is given by
where here we have:
Substituting, we find
f)
We can apply again the formula to find the escape velocity for the rocket:
Where this time we have:
, because the rocket is located at the Earth's surface, so its altitude is zero.
And substituting,
Learn more about gravitational force:
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