A ball of a mass 0.3 kg is released from rest at a height of 8 m. How fast is it going when it hits the ground? Acceleration due
2 answers:
In order to solve this problem, there are two equations that you need to know to solve this problem and pretty much all of kinematics. The first is that d=0.5at^2 (d=vertical distance, a=acceleration due to gravity and t=time). The second is vf-vi=at (vf=final velocity, vi=initial velocity, a=acceleration due to gravity, t=time). So to find the time that the ball traveled, isolate the t-variable from the d=0.5at^2. Isolate the t and the equation now becomes 
. Solving the equation where d=8 and a=9.8 makes the time 
=1.355 seconds. With the second equation, the vi=0 m/s, the vf is unknown, a=9.8 m/s^2 and t=1.355 sec. Substitute all these values into the equation vf-vi=at, this makes it vf-0=9.8(1.355). This means that the vf=13.28 m/s.
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1) -7.14 N
2) +2.70 N
3) 7.63 N
Explanation:
1)
In order to find the x-component of the resultant force, we have to resolve each force along the x-axis.
The first force is 8.00 N and is directed at an angle of 61.0° above the negative x axis in the second quadrant: this means that the angle with respect to the positive x axis is
so its x-component is
F₂ has a magnitude of 5.40 N and is directed at an angle of 52.8° below the negative x axis in the third quadrant: so, its angle with respect to the positive x-axis is
Therefore its x-component is
So, the x-component of the resultant force is
2)
In order to find the y-component of the resultant force, we have to resolve each force along the y-axis.
The first force is 8.00 N and is directed at an angle of 61.0° above the negative x axis in the second quadrant: as we said previously, the angle with respect to the positive x axis is
so its y-component is
F₂ has a magnitude of 5.40 N and is directed at an angle of 52.8° below the negative x axis in the third quadrant: as we said previously, its angle with respect to the positive x-axis is
Therefore its y-component is
So, the y-component of the resultant force is
3)
The two components of the resultant force representent the sides of a right triangle, of which the resultant force corresponds tot he hypothenuse.
Therefore, we can find the magnitude of the resultant force by using Pythagorean's theorem:
Where in this problem, we have:
is the x-component
is the y-component
And substituting, we find:
Answer:
g' = 10.12m/s^2
Explanation:
In order to calculate the acceleration due to gravity at the top of the mountain, you first calculate the length of the pendulum, by using the information about the period at the sea level.
You use the following formula:
(1)
l: length of the pendulum = ?
g: acceleration due to gravity at sea level = 9.79m/s^2
T: period of the pendulum at sea level = 1.2s
You solve for l in the equation (1):
Next, you use the information about the length of the pendulum and the period at the top of the mountain, to calculate the acceleration due to gravity in such a place:
g': acceleration due to gravity at the top of the mountain
T': new period of the pendulum
The acceleration due to gravity at the top of the mountain is 10.12m/s^2
Answer:
option (B)
Explanation:
Intensity of unpolarised light, I = 25 W/m^2
When it passes from first polarisr, the intensity of light becomes
Let the intensity of light as it passes from second polariser is I''.
According to the law of Malus
Where, θ be the angle between the axis first polariser and the second polariser.
I'' = 11.66 W/m^2
I'' = 11.7 W/m^2