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GREYUIT [131]
3 years ago
12

A firework is designed so that when it is fired directly upwards, it explodes and splits into three equal-massed parts at its pe

ak. Someone launches the firework directly upwards and measures the locations of two of the pieces of the firework. They find that one piece landed 2 meters to the left and another piece landed two meters behind them. Where did the third piece land? Assume that none of the three parts went further upward after the explosion.
Physics
1 answer:
Arturiano [62]3 years ago
4 0

Answer:

the third piece landed 2\,\sqrt{2}  meters in a direction 45 degrees from the observer's right towards the front

Explanation:

Due to conservation of momentum, the momentum of the third piece must add to the other two momenta in vector from to render zero  (initial momentum of the firework on a plane parallel to ground. Therefore the momentum components of the third piece must have a component to the right equal in magnitude to the momentum of the piece that traveled to the left, and a momentum component pointing to the front of the observer of equal magnitude to that of the piece that traveled behind the observer. Then the direction of the third momentum must be at 45 degrees from the observer's right towards the observer's front.

Also, the magnitude of a momentum vector of such components, is given by the Pythagorean theorem. Recall also that the magnitudes of the momentum vectors of the first two pieces must be equal since they traveled equal distances.

|P_3|=\sqrt{P_1^2+P_2^2} \\|P_3|=\sqrt{P^2+P^2}\\|P_3|=\sqrt{2P^2}\\|P_3|=P\sqrt{2}

Then the distance traveled by the third piece must also keep this proportionality:

D_3=\sqrt{2} \,\,D\\D_3=\sqrt{2} \,*\,2\,\,meters\\D_3=2\,\sqrt{2} \,\,meters

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A 2430 pound roller coaster starts from rest and is launched such that it crests a 105 ft high hill with a speed of 59 mph. The
Rudik [331]

Answer:

Explanation:

Given

Weight of roller coaster is W=2430\ pound

mass of roller coaster m=\frac{W}{g}=\frac{2430}{32.2}=75.45

Distance traveled by roller coaster d=396\ ft

drag force f_d=85\ pounds

velocity at top v=59 mph\approx 86.53\ ft/s

Suppose E is the initial energy

Conserving Energy at bottom and top

E=\frac{1}{2}mv^2+mgh+f_d\cdot d

E=0.5\times 75.45\times 86.53^2+2430\times 105+85\times 396

E=2.9\times 10^5\ foot-pound

5 0
3 years ago
What happens during destructive interference?
Masteriza [31]

They will subtract to form a combined wave with a lower amplitude

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3 years ago
A baseball pitcher throws a ball horizontally at a speed of 34.0 m/s. A catcher is 18.6 m away from the pitcher. Find the magnit
Sidana [21]

To develop this problem, it is necessary to apply the concepts related to the description of the movement through the kinematic trajectory equations, which include displacement, velocity and acceleration.

The trajectory equation from the motion kinematic equations is given by

y = \frac{1}{2} at^2+v_0t+y_0

Where,

a = acceleration

t = time

v_0 = Initial velocity

y_0 = initial position

In addition to this we know that speed, speed is the change of position in relation to time. So

v = \frac{x}{t}

x = Displacement

t = time

With the data we have we can find the time as well

v = \frac{x}{t}

t = \frac{x}{v}

t = \frac{18.6}{34}

t = 0.547s

With the equation of motion and considering that we have no initial position, that the initial velocity is also zero then and that the acceleration is gravity,

y = \frac{1}{2} at^2+v_0t+y_0

y = \frac{1}{2} gt^2+0+0

y = \frac{1}{2} gt^2

y = \frac{1}{2} 9.8*0.547^2

y = 1.46m

Therefore the vertical distance that the ball drops as it moves from the pitcher to the catcher is 1.46m.

6 0
3 years ago
the force that is exerted when a shopping cart is pushed. the forces that causes a metal ball to move toward a magnet
alexandr402 [8]

Answer:

The force that is exerted when a shopping cart is pushed is a type of push force, supplied by the muscles of the cart pusher's body.

The forces that causes a metal ball to move toward a magnet is a type of pull force that is as a result of the magnetic field forces.

Explanation:

Forces are divided into push forces that tends to accelerate a body away from the source of the force, and pull forces that accelerates the body towards the force source.

Examples of push forces includes pushing a cart, pushing a table, repulsion of two similar poles of a magnet etc. Examples of pull forces includes a attractive force between two dissimilar poles of a magnet, pulling a load by a rope, a dog pulling on a leash etc.

8 0
3 years ago
Read 2 more answers
Three identical train cars, coupled together, are rolling east at 1.8 m/s . A fourth car traveling east at 4.5 m/s catches up wi
Vedmedyk [2.9K]

Answer:

v = 1.98\ m/s

Explanation:

consider the mass of each train car be m

m₁ = m₂ = m₃ = m

speed of the three identical train

u₁ = u₂ = u₃ = 1.8 m/s

m₄ = m             u₄ = 4.5 m/s

m₅ = m              u₅ = 0 (initial velocity )

final velocity

v₁ = v₂ = v₃ = v₄ = v₅ = v

using conservation of momentum

m₁u₁ + m₂u₂ + m₃u₃ + m₄u₄ + m₅u₅ = m₁v₁ + m₂v₂ + m₃v₃ + m₄v₄ + m₅v₅

m (1.8 + 1.8 + 1.8 +4.5) = 5 m v

v = \dfrac{9.9}{5}

v = 1.98\ m/s

5 0
3 years ago
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