4
1 answer:
You might be interested in
Answer:
<em>The horizontal component of the velocity is 49.85 m/s.</em>
Explanation:
<u>Rectangular Components of a Vector</u>
A 2D vector can be expressed in several forms. The rectangular form gives its two components, one for each axis (x,y). The polar form gives the components as the pair (r,θ) being r the magnitude and θ the angle.
When the magnitude and angle of the vector are given, the rectangular components are calculated as follows:
Where v is the magnitude of the vector and θ is the angle with respect to the x positive direction.
The cart is moving at v=55 m/s at θ=25°, thus:
The horizontal component of the velocity is 49.85 m/s.
a) ,
The work done by the student in each trial is equal to the gravitational potential energy gained by the student:
where
m = 68 kg is the mass of the student
g = 9.8 m/s^2 is the acceleration of gravity
is the gain in height of the student
For the first student, , so the work done is
The second student runs up to the same height (3.5 m), so the work done by the second student is the same:
2) ,
The power exerted by each student is given by
where
W is the work done
t is the time taken
For the first student, and
, so the power exerted is
For the second student, and
, so the power exerted is
To solve this problem we will use the linear motion kinematic equations for which acceleration (in this case gravity) is described as the change in velocity in an instant of time. Subsequently through the energy conservation equations we will find the net height.
Let's start considering that the time is 1 second, therefore,
Now the acceleration would be given as
Since the final speed is zero, and the time elapsed to reach the height is 0.5 seconds (half of the entire route) we will have that the initial speed can be expressed in terms of gravity as
Now for energy conservation, the potential energy must be equal to the kinetic energy, therefore,
PE = KE
Replacing the previous value found,
Therefore the hegiht above the windows that the pot rises is 1.225m