How many feet are in a mile
2 answers:
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A) When the plane is flying straight down, there are three forces acting on it:
- the centripetal force
, directed toward the center of the circle (so, horizontally)
- the weight of the plane:
, downward, so vertically
- a third force, given by the propulsion of the plane, which is accelerating it towards the ground (because the problem says that the plane has an acceleration of a=12 m/s^2 towards the ground)
The radius of the circle is
, so the centripetal force acting on the plane is
On the vertical axis, we have two forces: the weight
and the other force F given by the propulsion. Since we know that their sum should generate an acceleration equal to
, we can find the magnitude of this other force F by using Newton's second law:
So, the net force acting on the plane will be the resultant of the centripetal force (acting in the horizontal direction) and the two forces W and F (acting in the vertical direction):
(b) The tangent of the angle with respect to the horizontal is the ratio between the sum of the forces in the vertical direction (taken with negative sign, since they are directed downward) and the forces acting in the horizontal direction, so:
And so, the angle is
- the centripetal force
- the weight of the plane:
- a third force, given by the propulsion of the plane, which is accelerating it towards the ground (because the problem says that the plane has an acceleration of a=12 m/s^2 towards the ground)
The radius of the circle is
On the vertical axis, we have two forces: the weight
and the other force F given by the propulsion. Since we know that their sum should generate an acceleration equal to
So, the net force acting on the plane will be the resultant of the centripetal force (acting in the horizontal direction) and the two forces W and F (acting in the vertical direction):
(b) The tangent of the angle with respect to the horizontal is the ratio between the sum of the forces in the vertical direction (taken with negative sign, since they are directed downward) and the forces acting in the horizontal direction, so:
And so, the angle is
Answer:
The object will travel 675 m during that time.
Explanation:
A body moves with constant acceleration motion or uniformly accelerated rectilinear motion (u.a.r.m) when the path is a straight line, but the velocity is not necessarily constant because there is an acceleration.
In other words, a body performs a u.a.r.m when its path is a straight line and its acceleration is constant. This implies that the speed increases or decreases uniformly.
In this case, the position is calculated using the expression:
x = xo + vo*t + ½*a*t²
where:
- x0 is the initial position.
- v0 is the initial velocity.
- a is the acceleration.
- t is the time interval in which the motion is studied.
In this case:
- x0= 0
- v0= 0 because the object is initially stationary
- a= 6
- t= 15 s
Replacing:
x= 0 + 0*15 s + ½*6 *(15s)²
Solving:
x=½*6 *(15s)²
x=½*6 *225 s²
x= 675 m
<u><em> The object will travel 675 m during that time.</em></u>