The perimeter of a rectangle is 66 feet. Find its dimensions assuming that its length is 9 feet less than twice its width.
1 answer:
Answer:
Length = 19 feet
Width = 14 feet
Explanation:
The perimeter, P, of a rectangle is given by
where l is the length and w is the width.
From the question, the length is 9 feet less than twice the width.
Substitute this in the equation for the perimeter.
Substitute for this in the equation for l.
Hence, the length is 19 feet and the width is 14 feet.
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Answer:
a) The weight and the normal force of the block has a magnitude of 137.298 newtons and the pull force exerted on the block has a magnitude of 98 newtons.
b) The final speed of the block of ice is 9.8 meters per second.
Explanation:
a) We need to calculate the weight, normal force from the ground to the block and the pull force. By 3rd Newton's Law we know that normal force is the reaction of the weight of the block of ice on a horizontal.
The weight of the block (), measured in newtons, is:
(1)
Where:
- Mass of the block of ice, measured in kilograms.
- Gravitational acceleration, measured in meters per square second.
If we know that and
, the magnitudes of the weight and normal force of the block of ice are, respectively:
And the pull force is:
The weight and the normal force of the block has a magnitude of 137.298 newtons and the pull force exerted on the block has a magnitude of 98 newtons.
b) Since the block of ice is on a frictionless surface and pull force is parallel to the direction of motion and uniform in time, we can apply the Impact Theorem, which states that:
(2)
Where:
,
- Initial and final speeds of the block, measured in meters per second.
- Horizontal net force, measured in newtons.
- Impact time, measured in seconds.
Now we clear the final speed in (2):
If we know that ,
,
and
, then final speed of the ice block is:
The final speed of the block of ice is 9.8 meters per second.
Answer:
<h2>10,000 J</h2>Explanation:
The kinetic energy of an object can be found by using the formula
m is the mass
v is the velocity
From the question we have
We have the final answer as
<h3>10,000 J</h3>Hope this helps you