5. Projectile A with mass m is launched at an angle of 20° above the horizontal with a speed v0. Projectile B also with mass m is launched from the same location at an angle of 70° above the horizontal, also with speed v0. Thus, both projectiles have the same initial total energy. a. Which projectile has a larger speed when it hits the ground or do they have the same speed? Explain using energy. b. Which projectile reaches a greater height? Given that both projectiles have the same initial energy, how is this possible?

Answers

Answer 1

Answer:

Answer:

a) They both have the same final speed.

b) Projectile B reaches a greater height

Explanation:

The initial total energy of both projectiles is the same, and since the initial height is zero, that initial energy is entirely kinetic energy:

$E_0=K_0=(1)/(2)mv_0^(2)$

Now, when the projectiles are going to reach the ground, their height also becomes zero, so the final energy is also entirely kinetic energy:

$E_f=K_f=(1)/(2)mv_f^(2)$

As stated in the conservation of mechanical energy, the final total energy has to be equal to the initial total energy, and then:

$E_0=E_f\n \n (1)/(2)mv_0^(2)=(1)/(2)mv_f^(2)\n\n\implies v_0=v_f$

Finally, since the initial speed is the same for both projectiles, they have the same speed when they hit the ground (a).

Next, we know that the height reached by a projectile depends only of their initial vertical velocity, nor their horizontal one. So, the projectile with the highest initial vertical velocity has to reach a greater height. We use trigonometry to calculate that:

$v_0_A_y=v_0\sin20\°=0.34v_0\n\nv_0_B_y=v_0\sin70\°=0.93v_0$

It means that projectile B has a higher initial vertical velocity, so it reaches a greater height (b).

This is possible because some of the kinetic energy of both projectiles is never transformed to gravitational potential energy (because is related to the horizontal velocity) and this amount of kinetic energy depends on the angle at which the projectile is launched. As their potential energies at the highest points are different, their maximum heights are, too.

Related Questions

An object is dropped from a height H above the ground. This free-falling object requires 1.02 s to travel the last 39 m before hitting the ground. From what height H above the ground did the object fall?
Different velocity-time graph lines are shown, displaying the behavior of multiple race carts along a linear track.Which description correctly identifies cart C?A) Has a positive acceleration and is speeding up. B) Moving with zero acceleration. C) Moving at a constant acceleration. D) Has a negative acceleration and is slowing down.
Can the normal force on an object be directed horizontally?
Which a vector quantity: speed or velocity?
Elements in the same group or family share important

Which particles make up the nucleus of an atom?

Answers

The particles that make up the nucleus of an atom are protons and neutrons.

The nucleus of an atom is composed of two main types of subatomic particles: protons and neutrons. Protons have a positive electric charge, while neutrons have no electric charge, making them neutral. These particles are relatively heavy compared to electrons, which orbit the nucleus.

The protons and neutrons are held together tightly in the nucleus by a strong force called the nuclear force or strong nuclear force. This force overcomes the repulsive force between positively charged protons, keeping the nucleus stable.

The number of protons in the nucleus determines the element's identity. For example, if an atom has one proton, it's hydrogen; if it has six protons, it's carbon, and so on. This number is called the atomic number. The sum of protons and neutrons in the nucleus is called the mass number.

To know more about nucleus here

brainly.com/question/34734091

#SPJ6

The nucleus of an atom contains the neutrons and protons, while electrons are on the outer shell.

Three quarterbacks challenged each other to a throwing competition. They want to see who can throw the ball the furthest. What SI unit would be most appropriate to measure the competition? Question 1 options: Celsius Gram Meter Liter

Answers

Answer:

Meter

Explanation:

The competition between the three quarterbacks is with respect to how far the ball would be thrown by each person, which is the distance covered by the ball. The thrown ball is an example of projectile, which would move over a certain distance.

With respect to the measure to be used in the competition, the appropriate SI unit is meter. This is the measure of length or distance covered.

If you know the components of a vector, what mathematical relationship can be used to find the magnitude of the vector?

Answers

You will always use Pythagoras theorem to find magnitude while given components of vector.
No matter if system that you are observing is 2D or 3D or higher (which is imaginery) pythagoras theorem will be applied.

Formula for determining magnitude is:
$M = √(x^ + y^2 + z^2 + ...)$

Number of turms inside square root you take depending on dimension of your system.

Iron has a density of 7.9 g/cm3. What is the mass of a cube of iron with the length of one side equal to 55.0 mm?

Answers

Density is a value for mass, such as kg, divided by a value for volume, such as m3. Density is a physical property of a substance that represents the mass of that substance per unit volume. To find the mass of the substance, we need to multiply the volume occupied by the substance.

Mass = Density x Volume
Mass = 7.9 g/cm^3 (5.5 cm)^3
Mass = 43.45 g

Answer:

Mass, m = 1.31 kg

Explanation:

It is given that,

Density of iron, $d=7.9\ g/cm^3$

Side of cube, a = 55 mm = 5.5 cm

We need to find the mass of the cube of iron. Mass per unit volume is called the density of the substance. It is given by :

$d=(m)/(V)$

$d=(m)/(a^3)$

$m=d* a^3$

$m=7.9* (5.5)^3$

m = 1314.36 grams

m = 1.31 kg

So, the mass of the iron cube is 1.31 kg. Hence, this is the required solution.

A radio wave has a frequency of 5.5 × 104 hertz and travels at a speed of 3.0 × 108 meters/second. what is its wavelength? a. 5.5 × 104 meters b. 5.0 × 103 meters c. 5.5 × 103 meters d. 3.0 × 108 meters

Answers

The wavelength of the radio wave is 5.5 × 10³ m. If the frequency of the wave is 5.5 × 10⁴ hertz and the speed of the wave is 3.0 × 10⁸ m/sec.

The speed(v) of a wave is the product of wavelength(λ) and the frequency(η). We can understand this relation by the definition of the speed, which is the distance travelled by the object in unit time. The unit of distance is meter, also the unit of the wavelength is meter. On the other hand the unit of frequency is sec⁻¹. So,

Speed of a wave(v) = wavelength(λ) × Frequency(η)

Wavelength(λ) = speed of the wave(v)/Frequency(η)

Wavelength(λ) = (3.0 × 10⁸)/(5.5 × 10⁴)

Wavelength(λ) = 5.5 × 10³ m

To know more about wavelength, here

brainly.com/question/13533093

#SPJ4

The frequency of wave A is 250 hertz and the wavelength is 30 centimeters. The frequency of wave B is260 hertz and the wavelength is 25 centimeters. Which is the faster wave?