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sergij07 [2.7K]
3 years ago
14

The path of an object projected at a 45 degree angle with initial velocity of 80 feet per second is given by the −32 2 function

h(x) = (80)2 x + x where x is the horizontal distance traveled and h(x) is the height in feet. Use the TRACE feature of your calculator to determine the height of the object when it has traveled 100 feet away horizontally.
Physics
1 answer:
Masteriza [31]3 years ago
6 0

Answer:

<h2>50 feet</h2>

Explanation:

Given the the path of an object at a 45° with initial velocity of 80 feet per second modeled by the equation h(x) = (-\dfrac{32}{80^2} )x^2 + x where;

x is the horizontal distance traveled and h(x) is the height in feet, if x is given as 100 ft, the height of the object will be gotten by simply substituting x = 100 into the modeled function as shown;

h(x) = (-\dfrac{32}{80^2} )x^2 + x\\\\h(100) = (-\dfrac{32}{80^2} )100^2 + 100\\\\h(100) = (-0.005 )100^2 + 100\\\\h(100) = (-0.005 )10,000 + 100\\\\h(100) = -50 + 100\\\\h(100) =50 feet

<em>Hence height of the object when it has traveled 100 feet away horizontally is 50 feet.</em>

<em></em>

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2. Two toy cars are involved in a race. Car A has mass m while car B has mass 2m. a. The two cars have the same force applied to
ArbitrLikvidat [17]

Answer:

a) The kinetic energy of the two cars is the same

the moment of car 2 is greater than the moment of car 1

b)  the kinetic energy of car 1 is greater than that of car 2

the moment of the two cars is the same

Explanation:

a) to know the kinetic energy of each car, we must find the speed, use Newton's second law to find the acceleration

Car 1

     F = m a

    a = F / m

Let's use kinematics to find the velocity after x = 1 m

       v² = v₀² + 2 a x

The initial speed is zero

       v = √ (2 F/m  x)

For the distance of x = 1 m

        v₁ = √ (2 F / m)

Car 2

      F = 2m a

      a = F / 2m

      v² = 2 a x

      v = √ (F/m  x)

 For x = 1 m

       v₂ = √(F / m)

Let's calculate the kinetic energy of each car

Car 1

      K₁ = ½ m v₁²

      K₁ = ½ m 2F / m

      K₁ = F

Car 2

      K₂ = ½ 2m v₂²

      K₂ = ½ 2m F / m

      K₂ = F

The kinetic energy of the two cars is the same

Let's calculate the moment

Car 1

   P₁ = m v₁

   P₁ = m √ (2F / m)

Car 2

    P₂ = 2m v²

    P₂ = 2m √(F / m)

We see that the moment of car 2 is greater than the moment of car 1

b) in this part the force is applied by t = 10 s

Acceleration is the same, let's find the speed

Car1

          v = v₀ + a t

          v = F / m t

          v₁ = F / m 10

Car 2

           v₂ = F / 2m 10

           v₂ = F / m 5

Let's calculate the kinetic energy of each car

Car 1

           K₁ = ½ m v₁²

           K₁ = ½ m (F / m 10)²

           K₁ = 50 F² / m

Car2

         K₂ = ½ 2m v₂²

         K₂ = m (F / m 5)²

         K₂ = 25 F² / m

In this case we see that the kinetic energy of car 1 is greater than that of car 2

Let's calculate the moment

Car 1

         P₁ = m v₁

         P₁ = m F / m 10

         P₁ = 10 F

 

Car 2

        P₂ = 2m v₂

        P₂ = 2m F / m 5

        P₂ = 10 F

In this case the moment of the two cars is the same

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The bell rings and a physics student heads to class. They stop to talk to a few friends. They slow
grin007 [14]

Answer:

420m

Explanation:

Given parameters:

Time  = 5minutes

Average speed  = 1.4m/s

Unknown:

Distance covered  = ?

Solution:

Speed is the rate of change of distance with time.

 Mathematically;

              Speed  = \frac{distance}{time}  

    Distance  = speed x time

 

Insert the parameters and solve;

   Convert the time to seconds;

              1 minute = 60s

               5 minute = 5  x 60 = 300s

So,

   Insert the parameters and find the distance;

     Distance  = 300 x 1.4  = 420m

3 0
3 years ago
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