Answer:
The change in the linear momentum is 225 kg.m/s and the force exerted on the tennis ball is 22,500 N.
Explanation:
What is linear momentum?
Linear momentum is the measure of a body's motion. Every object that has mass and moves at any velocity has linear momentum. Here are some examples of everyday life: falling balls, launching rockets, driving a car etc.
Now let's attack the problem.
First, we got to write the data down:
[tex]\bullet \quad m=3\,kg\\\\\bullet \quad v_o=40\,m/s\\\\\bullet \quad v=35\,m/s\\\\\bullet \quad \Delta t =0.01\,s[/tex]
We can write the change in linear momentum of the tennis ball as follows:
[tex]\Delta p = p-p_o[/tex]
The ball's momentum is equal to its mass times its velocity. Hence:
[tex]\Delta p= m\cdot v-m\cdot v_o[/tex]
Let's set the reference system as positive to left (see picture attached). For that purpose, when the ball bounces back its velocity changes sign.
Now, we are able to plug in the data:
[tex]\Delta p = 3\cdot 35 - 3\cdot(-40)\\\\\\\Delta p = 105+120\\\\\\\therefore \boxed{\Delta p =225\,kg\cdot m/s}[/tex]
To calculate the exerted force, we must apply the impulse theorem, which states that impulse equals the change in linear momentum of an object. We get:
[tex]\mathbb{I}=\Delta p[/tex]
Hence,
[tex]F \cdot \Delta t=\Delta p\\\\\\F\cdot 0.01=225\\\\\\F=\dfrac{225}{0.01}\\\\\\\therefore \boxed{F=22,\!500\,N}[/tex]
Conclusion: the change in linear momentum is 225 kg . m/s and the exerted force is 22,500 N.
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Brainly Team
