Question

Three 70-kg deer are standing on a flat 200-kg rock that is on an ice-covered pond. A gunshot goes off, and the deer scatter, with deer A running at (15 m/s)^i + (5.0 m/s)^j, deer B running at (-12 m/s)^i + (8.0 m/s)^j, and deer C running at (1.2 m/s)^i - (18.0 m/s)^j. What is the velocity of the rock on which they were standing?

a) (2.0 m/s)^i + (5.0 m/s)^j
b) (-4.8 m/s)^i + (-10.0 m/s)^j
c) (1.2 m/s)^i - (3.0 m/s)^j
d) (0 m/s)^i + (0 m/s)^j

Answer 1

The velocity of the rock on which the deer were standing is approximately 63.64 m/s.

Step-by-step explanation:

To find the velocity of the rock on which the deer were standing, we need to apply the principle of conservation of momentum. Since the deer were initially on a flat rock and there are no external forces, the total momentum before the gunshot is equal to the total momentum after the gunshot.

Let's denote the velocity of the rock as Vrock. The initial momentum is the sum of the momentum of the deer and the rock together, while the final momentum is the sum of the momentum of the deer and the rock separately.

Using the conservation of momentum equation, we can solve for Vrock:

Initial momentum = Final momentum

(3(70 kg)(15 m/s) + 3(70 kg)(5.0 m/s)) + (200 kg)(0 m/s) = (70 kg)(Vrock) + (70 kg)(-12 m/s) + (70 kg)(8.0 m/s)

Now, let's calculate the values:

(3150 kg·m/s + 1050 kg·m/s) = (70 kg)(Vrock) + (70 kg)(-12 m/s) + (70 kg)(8.0 m/s)

4200 kg·m/s = (70 kg)(Vrock) - (70 kg)(4 m/s)

4200 kg·m/s = Vrock(70 kg - 4 kg)

Vrock = 4200 kg·m/s / (66 kg)

Vrock = 63.64 m/s

The velocity of the rock on which the deer were standing is approximately 63.64 m/s.