Divergent plate boundaries are when plates

A block of mass m moving due east at speed v collides with and sticks to a block of mass 2m that is moving at the same speed vv

lapo4ka [179]

Answer:

30.36°

Explanation:

By using linear momentum; linear momentum can be expressed by the relation:

$mv_xi + mv_yj$

where ;

m= mass

$v_x$ = velocity of components in the x direction

$v_y$ = velocity of components in the y direction

If we consider the east as the positive x and north as positive y which is synonymous to what we usually have on a graph.

Then;

Initial momentum = $mvi + 2mvcos 45i + 2mvsin45 j$

= $(mv+2mvcos45)i + (2mvsin45)j$

However, the masses stick together after collision and move with a common velocity: $V_xi +V_yj$

∴ Final momentum = $3mv (V_xi +V_yj)$

= $3mV_xi + 3mV_yj$

From the foregoing ;

initial momentum = final momentum

$3mV_xi + 3mV_yj = (mv+2mvcos45)i+(2mvsin45j)$

So;

$3mV_x = mv + 2mv cos 45 \\\\3mV_y = 2mV sin 45$

$V_x = \frac{mv+2mvcos45 }{3m}\\\\V_x = \frac{v+2vcos45}{3}$

$V_y = \frac{2mvsin45}{3m} \\\\V_y = \frac{2vsin45}{3}$

Finally;

The required angle θ = $tan^{-1} = \frac{V_y}{V_x}$

θ = $tan^{-1} = \frac{\frac{2vsin45}{3}}{\frac{v+2v.cos45}{3}}$

θ = $tan^{-1} = \frac{2sin 45}{1+2cos45}\\\\$

θ = 30.36°

7 0

3 years ago

Does heating a cup of water allow it to dissolve more sugar? Temperature of the water is measured in degrees Centigrade. Amount

mixas84 [53]

Yes heating water allows it to dissolve more Sugars because the molecular distance increases and this distance can be covered by more sugar. In the given question, The independent variable would be the temperature of water.

Since to whatever temperature the water boils at the boiling temperature of does not change remains hundred degree. Rest all the variables can vary the weight of the amount of sugar with the variable in the temperature of Boiling of water to remain constant.

3 0

3 years ago

The following questions present a twist on the scenario above to test your understanding. Suppose another stone is thrown horizo

Ipatiy [6.2K]

The first part of the text is missing, you can find on google:

"A ball is thrown horizontally from the roof of a building 45 m. If it strikes the ground 56 m away, find the following values."

Let's now solve the different parts.

(a) 3.03 s

The time of flight can be found by analyzing the vertical motion only. The vertical displacement at time t is given by

$y(t) = h -\frac{1}{2}gt^2$

where

h = 45 m is the initial height

g = 9.8 m/s^2 is the acceleration of gravity

When y=0, the ball reaches the ground, so the time taken for this to happen can be found by substituting y=0 and solving for the time:

$0=h-\frac{1}{2}gt^2\\t=\sqrt{\frac{2h}{g}}=\sqrt{\frac{2(45)}{9.8}}=3.03 s$

(b) 18.5 m/s

For this part, we need to analyze the horizontal motion only, which is a uniform motion at constant speed.

The horizontal position is given by

$x=v_x t$

where

$v_x$ is the horizontal speed, which is constant

t is the time

At t = 3.03 s (time of flight), we know that the horizontal position is x = 56 m. By substituting these numbers and solving for vx, we find the horizontal speed:

$v_x = \frac{x}{t}=\frac{56}{3.03}=18.5 m/s$