A Bullet of a mass
10
g
is shot into a water melon of a mass
0.2
k
g
which is resting on a platform. At the time of impact, the bullet is travelling horizontally at
20
m
/
s
.
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bullet mass = 10 * 10^-3 = .01 kg
.01 * 20 = 0.21 * v
To find the final velocity of the watermelon and the bullet after the impact, we can use the principle of conservation of momentum. The total momentum before the impact is equal to the total momentum after the impact.
The momentum (p) of an object is given by the product of its mass (m) and its velocity (v): p = m * v.
Let's denote the mass of the bullet as mb = 10 g = 0.01 kg, the mass of the watermelon as mw = 0.2 kg, and the initial velocity of the bullet as vb = 20 m/s.
Before the impact, the bullet is the only object in motion, so the total momentum before the impact is simply the momentum of the bullet: pb_before = mb * vb.
After the impact, both the bullet and the watermelon move together. Let's assume their final velocity is vf. The total momentum after the impact is the sum of the momentum of the bullet and the momentum of the watermelon: p_after = (mb + mw) * vf.
According to the principle of conservation of momentum, pb_before = p_after:
mb * vb = (mb + mw) * vf.
Now we can plug in the values:
0.01 kg * 20 m/s = (0.01 kg + 0.2 kg) * vf.
Calculating this expression, we find:
0.2 kg * 20 m/s = 0.21 kg * vf.
4 = 0.21 * vf.
vf = 4 / 0.21
vf = 19.05 m/s (rounded to two decimal places).
So, the final velocity of the bullet and the watermelon after the impact is approximately 19.05 m/s.