On a very muddy football field, a 110 linebacker tackles an 75 halfback. Immediately before the collision, the linebacker is slipping with a velocity of 8.8 north and the halfback is sliding with a velocity of 7.2 east.
a) What is the magnitude of the velocity at which the two players move together immediately after the collision?
b) What is the direction of this velocity ?
so are there units with these numbers?
burr
1091.7
To find the magnitude of the velocity at which the two players move together immediately after the collision, we can use the principle of conservation of momentum.
a) The principle of conservation of momentum states that the total momentum of a system before a collision is equal to the total momentum after the collision, as long as no external forces are acting on the system.
The momentum of an object is defined as the product of its mass and velocity. So, we can calculate the initial momentum of the linebacker and the halfback separately:
Momentum of linebacker before collision = mass of the linebacker * velocity of the linebacker
Momentum of halfback before collision = mass of the halfback * velocity of the halfback
Since the linebacker is slipping with a velocity of 8.8 m/s north and the halfback is sliding with a velocity of 7.2 m/s east, we need to break down their velocities into their x and y-components.
For the linebacker:
Velocity of linebacker in the x-direction = 0 m/s (since it's slipping north)
Velocity of linebacker in the y-direction = 8.8 m/s north
For the halfback:
Velocity of halfback in the x-direction = 7.2 m/s east
Velocity of halfback in the y-direction = 0 m/s (since it's sliding east)
Now, we can calculate the momenta:
Momentum of linebacker before collision = mass of the linebacker * velocity of the linebacker
= 110 kg * 8.8 m/s north
= 968 kg·m/s north
Momentum of halfback before collision = mass of the halfback * velocity of the halfback
= 75 kg * 7.2 m/s east
= 540 kg·m/s east
The total momentum before collision is the vector sum of these two momenta:
Total momentum before collision = Momentum of linebacker before collision + Momentum of halfback before collision
To find the magnitude of the velocity at which the two players move together immediately after the collision, we can use the Pythagorean theorem to find the resultant momentum vector:
Magnitude of velocity = sqrt[(momentum in x-direction)^2 + (momentum in y-direction)^2]
b) To find the direction of this velocity, we can use the inverse tangent function (arctan) to determine the angle between the resultant momentum vector and the positive x-axis.
Direction of velocity = arctan(momentum in y-direction / momentum in x-direction)
By calculating these values using the given information, you can find the magnitude and direction of the velocity at which the two players move together immediately after the collision on the muddy football field.