A particle with velocity v(t)=1/t​−3, in m/s, moves in a straight line. Its initial displacement is known to be s(1)=1, in m. Find the position function s(t).

Final answer:

The maximum distance that a ball can be thrown at a speed of 20 m/s depends on the angle at which the ball is thrown. In ideal conditions and at a 45-degree angle, the theoretical maximum distance is approximately 40.57 meters.

Explanation:

The question is asking about the maximum distance you can throw a ball given an initial speed, which is a topic in Physics known as projectile motion. In an ideal condition, where air resistance is ignored, the maximum distance a projectile can travel is achieved when it is launched at an angle of 45 degrees.

However, we are missing a piece of information in this situation, which is the launch angle. Without knowing the angle at which the ball is thrown, we cannot accurately calculate the maximum distance. Theoretically, if the ball is thrown at an angle of 45 degrees, the distance (d) can be obtained using the formula for the range of a projectile: d = (v^2)/g, where v is the initial speed and g is the acceleration due to gravity. Substituting the value, d = (20^2)/9.81 = 40.57 meters. But this is an estimation and the value could change according to the actual circumstances when the ball is thrown.

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Answer:

θ = 41.8º

Explanation:

This is an internal total reflection exercise, the equation that describes this process is

         sin θ = n₂ / n₁

where n₂ is the index of the incident medium and n₁ the other medium must be met n₁> n₂

        θ = sin⁻¹ n₂ / n₁

let's calculate

       θ = sin⁻¹ (1.00 / 1.50)

       θ = 41.8º

Answer:

Yes

Explanation:

Neglecting air resistance, the total mechanical energy of the system would be conserved because the two forces acting on the weight are the spring force and the gravitational force, and both are conservative in nature.

The amount of thermal energy that is created in the slope and the tube during the ascent is 19680 Joules.

Given the following data:

• Total mass = 80 kg

• Tension = 360 Newton

• Height = 30 meters

• Displacement = 120 meters

To find the amount of thermal energy that is created in the slope and the tube during the ascent:

By applying the Law of Conservation of Energy:

Where:

• K.E is the kinetic energy.

• P.E is the potential energy.

• T.E is the thermal energy.

Since the rider and his tube are pulled at a constant speed, K.E is equal to zero (0).

Therefore, the formula now becomes:

For the work done:

Work done = 43,200 Joules.

For P.E:

P.E = 23,520 Joules.

Now, we can find the amount of thermal energy:

T.E = 19680 Joules.

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Answer:

Explanation:

GIVEN DATA:

Total mass ( rider  + his tube) = 80 kg

tension  Force = 360 N

height of slope  =  30 m

length of slope = 120 m

we know that thermal energy is given as

E_{th}  = W- Ug

W= F*d = (360N*120m)= 43200 J        

Ug= m*g*h = (80kg*9.8m/s2*30m) = 23520 J