Refer to the diagram shown below.
In 2.4 hours, the distance traveled by the first airplane heading a 51.3° at 750 mph is
a = 750*2.4 = 1800 miles.
The second airplane travels
b = 620*2.4 = 1488 mile
The angle between the two airplanes is
163° - 51.3° = 111.7°
Let c = the distance between the two airplanes after 2.4 hours.
From the Law of Cosines, obtain
c² = a² + b² - 2ab cos(111.7°)
= 3.24 x 10⁶ + 2.2141 x 10⁶
c = 2335.41 miles
Answer: 2335.4 miles
The force of gravity between two objects is given by:
where
G is the gravitational constant
m1 and m2 are the masses of the two objects
r is their separation
In this problem, the mass of the object is
, while the Earth's mass is
. Their separation is
, therefore the gravitational force exerted on the object is
Answer:
a) 4 289.8 J
b) 4 289.8 J
c) 6 620.1 N
d) 411 186.3 m/s^2
e) 6 620.1 N
Explanation:
Hi:
a)
The kinetic energy of the bullet is given by the following formula:
K = (1/2) m * v^2
With
m = 16.1 g = 1.61 x 10^-2 kg
v = 730 m/s
K = 4 289.8 J
b)
the work-kinetic energy theorem states that the work done on a system is the same as the differnce in kinetic energy of the same. Since the initial state of the bullet was at zero velocity (it was at rest) Ki = 0, therefore:
W = ΔK = Kf - Ki = 4 289.8 J
c)
The work done by a force is given by the line intergarl of the force along the trayectory of the system (in this case the bullet).
If we consider a constant force (and average net force) directed along the trayectory of the bullet, the work and the force will be realted by:
W = F * L
Where F is the net force and L is the length of the barrel, that is:
F = (4 289.8 J) / (64.8 cm) = (4 289.8 Nm) / (0.648 m) = 6620.1 N
d)
The acceleration can be found dividing the force by the mass:
a = F/m = (6620.1 N) /(16.1 g) = 411 186.3 m/s^2
e)
The force will have a magnitude equal to c) and direction along the barrel towards the exit
Answer: The angle of inclination is nearly 30°
Explanation:
For a body on an inclined plane, the coefficient of friction between the body and the plane is equal to the ratio of the moving force applied to the body to the frictional force acting on the body.
If uK coefficient of friction;
Fm is the moving force
R is the normal reaction on the body
Mathematically uK = Fm/R
Fm = WSin(theta)
R = Wcos(theta)
uK = Wsin(theta)/Wcos(theta)
uK = tan(theta)
theta = arctan(uK)
If uK is 0.58
theta = arctan0.58
theta = 30°
The angle of the inclined will be 30°
