Suppose an object is moving 2.1 m/s north on a river, but the river is flowing to the east at a velocity of 1.2 m/s. What is the
1 answer:
Answer:
2.4 m/s
Explanation:
Given:
Velocity of the object moving north = 2.1 m/s
Velocity of the river moving eastward = 1.2 m/s
The resultant velocity is the vector sum of the velocities of object and river.
Since the directions of velocity of object and river are perpendicular to each other, the magnitude of the resultant velocity is obtained using Pythagoras Theorem.
The velocities are the legs of the right angled triangle and the resultant velocity is the hypotenuse.
The magnitude of the resultant velocity (R) is given as:
Therefore, the resultant velocity has a magnitude of 2.4 m/s.
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We need to write down momentum and energy conservation laws, this will give us a system of equation that we can solve to get our final answer. On the right-hand side, I will write term after the collision and on the left-hand side, I will write terms before the collision.
Let's start with energy conservation law:
This equation tells us that kinetic energy of two carts before the collision and 3 quarters of explosion energy is beign transfered to kinetic energy of the cart after the collision.
Let's write down momentum conservation law:
Because both carts have the same mass we can cancel those out:
Now we have our system of equation that we have to solve:
Part A
We need to solve our system for
. We will solve second equation for 
and then plug that in the first equation.
Now we have to plug this in the first equation:
We will multiply the first equation with 2 and divide by m:
Now we plug in the second equation into first one:
We end up with quadratic equation that we have to solve, I won't solve it by hand.
Coefficients are:
Solutions are:
Part B
We do the same thing here, but we must express from momentum equation:
Now we plug this into our energy conservation equation:
Again we end up with quadratic equation. Coefficients are:
Solutions are:
Let's start with energy conservation law:
This equation tells us that kinetic energy of two carts before the collision and 3 quarters of explosion energy is beign transfered to kinetic energy of the cart after the collision.
Let's write down momentum conservation law:
Because both carts have the same mass we can cancel those out:
Now we have our system of equation that we have to solve:
Part A
We need to solve our system for
Now we have to plug this in the first equation:
We will multiply the first equation with 2 and divide by m:
Now we plug in the second equation into first one:
We end up with quadratic equation that we have to solve, I won't solve it by hand.
Coefficients are:
Solutions are:
Part B
We do the same thing here, but we must express
Now we plug this into our energy conservation equation:
Again we end up with quadratic equation. Coefficients are:
Solutions are:
The acceleration of the snowboarder is down along the incline
Explanation:
To find the acceleration of the snowboard, we have to analyze the forces acting along the direction parallel to the incline.
There is only one force acting in this direction, and it is the component of the weight parallel to the incline, given by
where
m = 75.0 kg is the mass of the man
is the acceleration of gravity
is the angle of the incline
Substituting, we find that the net force along the incline is:
According to Newton's second law, the net force on the snowboard is equal to the product between his mass and his acceleration:
where a is the acceleration. Therefore, solving for a, we find
And the direction of this acceleration is down along the incline.
Learn more about acceleration and Newton's second law:
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