Assume no air resistance, and g = 9.8 m/s².
Let
x = angle that the initial velocity makes with the horizontal.
u = 30 cos(x), horizontal velocity
v = 30 sin(x), vertical launch velocity
The horizontal distance traveled is 55 m, therefore the time of flight is
t = 55/[30 cos(x)] = 1.8333 sec(x) s
With regard to the vertical velocity, and the time of flight,obtain
[30 sin(x)]*(1.8333 sec(x)) + (1/2)*(-9.8)*(1.8333 sec(x))² = 0
55 tan(x) - 16.469 sec²x = 0
55 tan(x) - 16.469[1 + tan²x] = 0
16.469 tan²x - 55 tan(x) + 16.469 = 0
tan²x - 3.3396 tan(x) + 1 = 0
Solve with the quadratic formula.
tan(x) = 0.5[3.3396 +/- √(7.153)] = 3.007 or 0.3326
Therefore
x = 71.6° or x = 18.4°
The time of flight is
t = 1.8333 sec(x) = 5.8096 s or 1.932 s
The initial vertical velocity is
v = 30 sin(x) = 28.467 m/s or 9.468 m/s
The horizontal velocity is
u = 30 cos(x) = 9.467 m/s or 28.469 m/s
If t = 5.8096 s,
u*t = 9.467*5.8096 = 55 m (Correct)
or
u*t = 28.469*15.8096 = 165.4 m (Incorrect)
Therefore, reject x = 18.4°. The correct solution is
t = 5.8096 s
x = 71.6°
u = 9.467 m/s
v = 28.467 m/s
The height from which the ball was thrown is
h = 28.467*5.8096 - 0.5*9.8*5.8096² = -110.4 m
The ball was thrown from a height of 110.4 m
Answer: h = 110.4 m
Answer:
Explanation:
At some distance from the Earth the force of attraction due to moon is balanced by the force due to Moon
so we will have
now we have
so we will have
Now by energy conservation
Answer:
The acceleration is 14.28 km/h^2
Explanation:
Step one:
Given data
initial speed u= 0 km/h
final speed v= 140km/h
time t= 9.8 seconds
Required
The acceleration of the car
Step two:
From a= v-u/t
substitute
a= 140-0/9.8
a=140/9.8
a=14.28 km/h^2
Answer:
Correct options are C. As food is digested, molecule bonds are broken, allowing new molecules to form that can be used by our bodies.
D. Energy stored in organic fuels are used for heat and electricity/ When batteries are connected to a circuit, a reaction occurs inside the cell producing electrical energy.
Explanation:
The breakdown of food leads to the release of chemical energy which was first stored in food. This energy is used to drive necessary functions of the body. A series of chemical reactions are involved in the breakdown of food and changing them into useful components for the cell.
Chemical energy is stored in circuits. When the battery is connected to a circuit, the chemical energy gets transferred into electrical energy.
Answer:
Approximately 
.
Explanation:
This question suggests that the rotation of this object slows down "uniformly". Therefore, the angular acceleration of this object should be constant and smaller than zero.
This question does not provide any information about the time required for the rotation of this object to come to a stop. In linear motions with a constant acceleration, there's an SUVAT equation that does not involve time:
,
where
is the final velocity of the moving object, 
is the initial velocity of the moving object,
is the (linear) acceleration of the moving object, and
is the (linear) displacement of the object while its velocity changed from to .
The angular analogue of that equation will be:
, where
and 
are the initial and final angular velocity of the rotating object,
is the angular acceleration of the moving object, and
is the angular displacement of the object while its angular velocity changed from to .
For this object:
, whereas
.
The question is asking for an angular acceleration with the unit 
. However, the angular displacement from the question is described with the number of revolutions. Convert that to radians:
.
Rearrange the equation and solve for :
.
