An object is released from rest near and above Earth’s surface from a distance of 10m. After applying the appropriate kinematic

The formula for range is:

Given values are:

where θ equals 14.1 degrees

Using the equation above,

The calculated range is 66.7 meters.

Therefore, the range is approximately 66.1 meters.

Answer:

C) True. The distance S increases over time, with v₁ = gt and v₂ = g (t-t₀), illustrating that v₁> v₂ for the same t.

Explanation:

We have a set of statements to evaluate for correctness. The most effective approach is to examine the problem in detail.

Using the equation for vertical launch, we acknowledge that the positive direction signifies downward movement.

Stone 1

    y₁ = v₀₁ t + ½ g t²

    y₁ = 0 + ½ g t²

Stone 2

Released shortly thereafter, let's assume a delay of one second, we can utilize the same timing mechanism

     t ’= (t-t₀)

    y₂ = v₀₂ t ’+ ½ g t’²

    y₂ = 0 + ½ g (t-t₀)²

    y₂ = + ½ g (t-t₀)²

We can now calculate the separation distance between the two stones, which is applicable for t> = to

    S = y₁ -y₂

    S = ½ g t²– ½ g (t-t₀)²

    S = ½ g [t² - (t² - 2 t t₀ + t₀²)]  

    S = ½ g (2 t t₀ - t₀²)

    S = ½ g t₀ (2 t - t₀)

This represents the distance between the two stones over time, with the coefficient outside the parentheses being constant.

For t < to, the first stone remains stationary while the distance grows.

For t > = to, the expression (2t/to-1) yields a value greater than 1, indicating that the distance expands as time progresses.

We can now analyze the different statements

A) false. The height difference increases over time.

B) False S increases.

C) It is true that S increases over time, with v₁ = gt and V₂ = g (t-t₀) indicating v₁> v₂ at the same t.

The change in momentum (i.e., impulse) from the car during the collision remains constant regardless of whether an airbag is present. This is because the car's mass is unchanged, and the velocity change remains the same. Therefore, if the force is constant as F and reduced by a factor of 110, it follows that the collision duration must increase by the same factor when the airbag is utilized.

Answer:

b) TA = TB = TC

Explanation:

• When the blocks are brought into contact and isolated from the environment, they will exchange heat until they achieve thermal equilibrium.
• During this exchange, the hotter body will lose heat, which will be gained by the cooler body.
• The equilibrium state will be established once this equation is satisfied:

       

• Substituting the initial temperatures T₀A = 300º C and T₀B = 400ºC, while simplifying for equal block masses mA = mB, enables us to solve for the final temperature, Tfin:

       

• At equilibrium, when both blocks combine, they will yield a uniform final temperature of 350ºC.
• When block C, also at this temperature, makes contact, all three blocks will simultaneously reflect this final temperature of 350 ºC.
• Therefore, option b) is correct.