Answer:
11 m/s
Explanation:
The impulse given to the ball is equal to its change in momentum:
[tex]I=\Delta p=m \Delta v= m(v_f -v_i)[/tex]
where
m=2.0 kg is the mass of the ball
[tex]v_i=3.0 m/s[/tex] is the initial velocity of the ball
[tex]v_f[/tex] is the final velocity of the ball
[tex]I=16 Ns[/tex] is the impulse
If we re-arrange the formula and we replace the numbers, we can find the final velocity:
[tex]v_f = \frac{I}{m}+v_i=\frac{16 Ns}{2.0 kg}+3.0 m/s=11 m/s[/tex]
The correct answer to the question is 11 m/s.
CALCULATION:
The mass of the ball is given as m = 2.0 kg.
The impulse exerted on the ball is 16 N-s.
The initial velocity of the ball u = 3 m/s.
We are asked to calculate the final velocity v.
The impulse of a ball is defined as the product of force with time. On the other hand, it can be defined as the change in momentum of a body.
Mathematically it can be written as -
Impulse = mv - mu = dp.
Here, p stands for the momentum.
From above we see that impulse = 16 N-s.
⇒ mv - mu = 16 N-s
⇒ m(v-u) = 16 N-s
⇒ v - u = [tex]\frac{16}{m}[/tex]
= [tex]\frac{16}{2}\ m/s[/tex]
= 8 m/s
⇒ v = u + 8 m/s
= 3.0 m/s + 8.0 m/s
= 11 m/s [ans]
