Two 72.0 kg hockey players skating at 7.00 m/s collide and stick together. If the angle between their initial directions was 120 degrees, what is their speed after the collision?
draw the figure. Notice symettry will allow for two components of momentum perpendicular to the line of symettry will cancel, so what is left is 2*72*7*cos60
A 74-kg canoeist stands in the middle of her 18-kg canoe. The canoe is 3.0 m long, and the end that is closest to land is 2.5 m from the shore. The canoeist now walks toward the shore until she comes to the end of the canoe.
calculate the distance from the canoeist to shore.
To find the speed after the collision, we can use the principles of conservation of momentum and conservation of kinetic energy.
The initial momentum before the collision can be calculated by adding the individual momenta of the two hockey players. Momentum is a vector quantity, so we need to consider both the magnitude (speed) and direction.
First, let's calculate the individual momenta of the hockey players.
Player 1:
Mass (m1) = 72.0 kg
Speed (v1) = 7.00 m/s
Player 2:
Mass (m2) = 72.0 kg
Speed (v2) = 7.00 m/s
The momentum (p) of each player is given by the equation: p = m * v.
P1 = m1 * v1 = 72.0 kg * 7.00 m/s
P2 = m2 * v2 = 72.0 kg * 7.00 m/s
Now, let's resolve the momenta into their x and y components. Since the angle between their initial directions is 120 degrees, we can find the x and y components using trigonometry.
For player 1:
Px1 = P1 * cos(120°)
Py1 = P1 * sin(120°)
For player 2:
Px2 = P2 * cos(120°)
Py2 = P2 * sin(120°)
Next, let's calculate the total momentum in the x-direction (horizontal).
Ptotal_x = Px1 + Px2
And the total momentum in the y-direction (vertical).
Ptotal_y = Py1 + Py2
Since they collide and stick together, their final momentum in the x-direction will be the sum of their individual x-components.
P_final_x = Ptotal_x
Their final momentum in the y-direction will be the sum of their individual y-components.
P_final_y = Ptotal_y
Now, we can calculate the magnitude of the total momentum (P_total) using Pythagoras' theorem.
P_total = sqrt((P_final_x)^2 + (P_final_y)^2)
This total momentum before the collision is equal to the total momentum after the collision, since momentum is conserved.
P_total = P_after_collision = m_total * v_after_collision
Since the masses of the two hockey players are the same (m1 = m2 = 72.0 kg), we can substitute the total mass.
P_total = (m1 + m2) * v_after_collision
Rearranging the equation, we get:
v_after_collision = P_total / (m1 + m2)
Now, plug in the known values to find the final speed after the collision.