Bruce has a momentum of 430kg m/s and is running at 7.8m/s. What is Bruce's mass?
2 answers:
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Answer:
The polar coordinate of is
.
Explanation:
Given a point in rectangular form, that is , its polar form is defined by:
(1)
Where:
- Norm, measured in meters.
- Direction, measured in sexagesimal degrees.
The norm of the point is determined by Pythagorean Theorem:
(2)
And direction is calculated by following trigonometric relation:
(3)
If we know that and
, then the components of coordinates in polar form is:
Since and
, direction is located at 3rd Quadrant. Given that tangent function has a period of 180º, we find direction by using this formula:
The polar coordinate of is
.
To solve this problem it is necessary to apply the concepts related to Normal Force, frictional force, kinematic equations of motion and Newton's second law.
From the kinematic equations of motion we know that the relationship of acceleration, velocity and distance is given by
Where,
Final velocity
Initial Velocity
a = Acceleration
x = Displacement
Acceleration can be expressed in terms of the drag coefficient by means of
Frictional Force
Force by Newton's second Law
Where,
m = mass
a= acceleration
Kinetic frictional coefficient
g = Gravity
Equating both equation we have that
Therefore,
Re-arrange to find x,
The distance traveled by the car depends on the coefficient of kinetic friction, acceleration due to gravity and initial velocity, therefore the three cars will stop at the same distance.
First we need to find the speed of the dolphin sound wave in the water. We can use the following relationship between frequency and wavelength of a wave:
where
v is the wave speed
its wavelength
f its frequency
Using
and 
, we get
We know that the dolphin sound wave takes t=0.42 s to travel to the tuna and back to the dolphin. If we call L the distance between the tuna and the dolphin, the sound wave covers a distance of S=2 L in a time t=0.42 s, so we can write the basic relationship between space, time and velocity for a uniform motion as:
and since we know both v and t, we can find the distance L between the dolphin and the tuna:
where
v is the wave speed
f its frequency
Using
We know that the dolphin sound wave takes t=0.42 s to travel to the tuna and back to the dolphin. If we call L the distance between the tuna and the dolphin, the sound wave covers a distance of S=2 L in a time t=0.42 s, so we can write the basic relationship between space, time and velocity for a uniform motion as:
and since we know both v and t, we can find the distance L between the dolphin and the tuna: