Answer:
They will both hit the ground at the same time
Explanation:
<span>The primary reason a light bulb emits light is due to the heating of the resistance in the filament of the light bulb. In fact, the power dissipated in a resistor is given by
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<span>where I is the current and R the resistance. The larger the resistance or the current in the resistor, the larger the power dissipated. Due to this dissipation of power, the temperature of the filament becomes very high, and the resistance becomes incandescent, emitting light.</span>
<span>31.3 m/s
Since the water balloon is being launched at a 45 degree angle, the horizontal and vertical speeds will be identical. Also the time the balloon takes to reach its peak altitude will match the time it takes to fall. So let's create a few expressions about what we know.
Distance the water balloon travels at velocity v for time t
d = vt
Total time required for the entire trip is double since the balloon goes up, then goes down
t = 2v/a
Now let's plug in the numbers we have, assuming the acceleration due to gravity is 9.8 m/s^2
t = 2v/9.8
100 = vt
Substitute 2v/9.8 for t in the 2nd formula
100 = v(2v/9.8)
Solve for v.
100 = v(2v/9.8)
100 = 2v^2/9.8
980. = 2v^2
490 = v^2
22.13594 = v
So we now know that both the horizontal velocity and vertical velocity needed is 22.13594 m/s. Let's verify that
2*22.13594 / 9.8 = 4.51754
So it will take 4.51754 second for the balloon to hit the ground after being launched.
4.51754 * 22.13594 = 100
And during that time it will travel 100 meters horizontally.
But we need to know the total velocity. And the Pythagorean theorem comes to the rescue. Just square the 2 velocities, add them together, and take the square root. We already know the square is 490 from the work above, so
sqrt(490+490) = sqrt(980) = 31.30495 m/s</span>
Answer:
Explanation:
In the x direction the force will be
½(-w₀)L/2 = -¼w₀L
acting ⅔(L/2) = L/3 below the x axis.
In the y direction the force will be
½(-w₀)L + ½w₀L/2 = -¼w₀L
the magnitude of the resultant will be
F = w₀L √((-¼)² + (-¼)²) = w₀L√⅛
in the direction
θ = arctan(-¼w₀L / -¼w₀L) = 225°
to find the distance, we balance moments
(w₀L√⅛)[d] = ½(w₀)L[⅔L] + ¼w₀L[⅔L/2] - ¼w₀L[L - ⅓L/2]
(√⅛)[d] = ½ [⅔L] + ¼ [⅔L/2] - ¼ [L - ⅓L/2]
(√⅛)[d] = ½[⅔L] + ¼[⅔L/2] - ¼[L - ⅓L/2]
(√⅛)[d] = ⅓L + ⅟₁₂L - ¼L + ⅟₂₄L
(√⅛)[d] = 5L/24
d = 5L/24 / (√⅛)
d = 5√⅛L/3
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