You and your friend, both of mass 70 kg, are playing catch with a frisbee on frictionless ice. Initially, you are both at rest. You throw a 0.175 kg frisbee at 10 m/s horizontally at your friend, who catches it. After they catch the frisbee, what is the relative velocity between you and your friend in m/s?
m₁=m= 70 kg
m₃=0.175 kg, v₃=10 m/s
Let v₃ be positive and directed to the right
0= - m₁v₁+m₃v₃
v₁=m₃v₃/m₁=0.175•10/70=0.025 m/s (directed to the left)
m₃v₃ =(m₂+m₃)v
v= m₃v₃/(m₂+m₃)=0.175•10/(70+0.175)=0.0249 m/s (directed to the right)
V(relative) =
=v₁+v=0.025+0.0249 =0.0499 m/s
thankyou
To determine the relative velocity between you and your friend after they catch the frisbee, we need to consider the conservation of momentum. The total momentum before the catch should be equal to the total momentum after the catch.
Let's break down the problem step by step:
1. Determine the initial momentum before the catch:
The momentum of the frisbee is given by its mass (0.175 kg) multiplied by its velocity (10 m/s). Therefore, the momentum of the frisbee before the catch is:
Momentum of frisbee before catch = mass × velocity
= 0.175 kg × 10 m/s
= 1.75 kg·m/s
Since both you and your friend are initially at rest, your combined initial momentum is 0 kg·m/s.
2. Determine the final momentum after the catch:
The final momentum after the catch is the sum of the frisbee's momentum and the combined momentum of you and your friend. Let's assume that the relative velocity between you and your friend is v.
Momentum of frisbee after catch = mass × velocity
= 0.175 kg × (-v) (the negative sign is because the frisbee is moving in the opposite direction)
= -0.175v kg·m/s
Momentum of you and your friend after catch = mass × velocity
= 140 kg × (-v) (each of you has a mass of 70 kg)
= -140v kg·m/s
The total momentum after the catch is the sum of the above two momenta:
Total momentum after catch = (momentum of frisbee after catch) + (momentum of you and your friend after catch)
= -0.175v kg·m/s + (-140v) kg·m/s
= -140.175v kg·m/s
3. Apply the conservation of momentum:
According to the law of conservation of momentum, the total momentum before the catch should be equal to the total momentum after the catch:
Total momentum before catch = Total momentum after catch
Since the initial momentum is 0 kg·m/s, we can equate the two expressions:
0 kg·m/s = -140.175v kg·m/s
To solve for v, divide both sides by -140.175 kg·m/s:
0 = v
This means that the relative velocity between you and your friend after they catch the frisbee is 0 m/s. In other words, you and your friend are at rest relative to each other.