A vector has an x-component of 19.5m and a y-component of 28.4m. Find the magnitude and direction of the vector
1 answer:
Answer:
34.5 m at 55.5 degrees above the positive x-axis
Explanation:
Resolving a vector means finding its components along two perpendicular axis: most commonly, they are chosen as the x and y axis.
In this problem, we have a vector whose components are:
x -component: 19.5 m
y- component: 28.4 m
The two components are perpendicular to each other: this means that we can find the magnitude of the vector by using the Pythagorean theorem
The direction, instead, can be found by using the following formula:
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The launch velocity is 4.8 m/s
Explanation:
We can solve this problem by applying the law of conservation of energy. In fact, the mechanical energy of the hopper (equal to the sum of the potential energy + the kinetic energy) is conserved. So we can write:
where:
is the initial potential energy, at the bottom
is the initial kinetic energy, at the bottom
is the final potential energy, at the top
is the final kinetic energy, at the top
We can rewrite the equation as:
where:
m is the mass of the hopper
is the acceleration of gravity
is the initial height
u is the launch speed of the hopper
is the maximum altitude reached by the hopper
v = 0 is the final speed (which is zero when the hopper reaches the maximum height)
Solving the equation for u, we find the launch speed of the hopper:
Learn more about kinetic energy and potential energy:
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