Answer:
1.) h = 164.8 m
2.) U = 49.1 m/s
3.) t = 1.43 seconds
Explanation:
1.) A soccer ball is dropped from the top of a building. It takes 5.8 seconds to fall to the ground. The height of the building is...?
Since the soccer ball is dropped from the building, the initial velocity U will be equal to zero
Using second equation of motion
h = Ut + 1/2gt^2
Substitutes the time into the formula
h = 1/2 × 9.8 × 5.8^2
h = 164.8 m
2. The Falcon 9 launches to a height of 123 meters. What is its vertical initial velocity?
At maximum height final velocity = 0
Using the third law of motion
V^2 = U^2 - 2gH
0 = U^2 - 2 × 9.8 × 123
U^2 = 2410.8
U = 49.1 m/s
3. An apple falls from rest off a 10.m m tree. How long will it take before it hits the ground?
Since the apple fall from rest, the initial velocity U will be equal to zero
Using the second equation of motion,
h = Ut + 1/2gt^2
substitute all the parameters into the formula
10 = 1/2 × 9.8 × t^2
10 = 4.9t^2
t^2 = 10/4.9
t^2 = 2.04
t = 1.43 seconds
The gravitational force of the shell exerts is 4.25m x 10¯¹² N.
We need to know about gravitational force to solve this problem. The gravitational force is the force caused by two masses of objects. The magnitude of gravitational force can be determined as
F = G.m1.m2 / R²
where F is the gravitational force, G is the gravitational constant (6.674 × 10¯¹¹ Nm²/kg²), m1 and m2 are the mass of the object and R is the radius.
From the question above, we know that
m1 = 1.6 kg
m2 = m
R = 5.01 m
By substituting the following parameters, we get
F = G.m1.m2 / R²
F = 6.674 × 10¯¹¹ . 1.6 . m / 5.01²
F = 4.25m x 10¯¹² N
where m is the mass of the shell
For more on gravitational force at: brainly.com/question/19050897
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Answer:
<em>The speed of the projectile when it impacts the ground is 1000 m/s</em>
Explanation:
<u>Vertical Launch</u>
When an object is launched vertically and upwards it starts to move at an initial speed vo, then the acceleration of gravity makes that speed to reduce until it reaches 0. The object has reached its maximum height. Then, it starts to move downwards in free fall, with initial speed zero and gradually increasing it until it reaches the ground level. We will demonstrate that the speed it has when impacts the ground is the same (and opposite) as the initial speed vo.
The speed when the object is moving upwards is given by

The time it takes to reach the maximum height is when vf=0, i.e.

solving for t

The maximum height reached is

Then, the object starts to fall. The object's height is given by

where t' is the time the object has traveled downwards. The height will be 0 again when

Solving for t'

We can see the time it takes to reach the maximum height is the same it takes to return to ground level. Of course, the speed when it happens is

Thus, the speed of the projectile when it impacts the ground is 1000 m/s
Answer:
The tension of the string is 41.876 N
Explanation:
Given;
length of the string, L = 2.11 m
mass of the string, m = 19.5 g = 0.0195 kg
frequency of the wave, f = 440 Hz
wavelength, λ = 15.3 cm = 0.153 m
The velocity of the wave is given by;
v = fλ
v = 440 x 0.153
v = 67.32 m/s
Also the velocity of the wave is given by

where;
μ is mass per unit length = 0.0195 / 2.11 = 0.00924 kg/m
T is the tension of the string
T = v²μ
T = (67.32)²(0.00924)
T = 41.876 N
Therefore, the tension of the string is 41.876 N