Answer:
[tex]a_2=24.5\ \text{m/s}^2[/tex] towards right
[tex]a_1=2.1875\ \text{m/s}^2[/tex] towards left
Explanation:
[tex]m_1[/tex] = Mass of skater = 56 kg
[tex]m_2[/tex] = Mass of ball = 5 kg
v = Final velocity of ball = 7 m/s
u = Initial velocity of ball = 0
s = Distance the ball moved in the hand of the skater = 1 m
Moving left is considered and moving right is considered positive.
From kinematic equations of motion we have
[tex]v^2-u^2=2as\\\Rightarrow a=\dfrac{v^2-u^2}{2s}\\\Rightarrow a=\dfrac{7^2-0^2}{2\times 1}\\\Rightarrow a=24.5\ \text{m/s}^2[/tex]
So, the ball will move towards right with a magnitude of acceleration [tex]a_2=24.5\ \text{m/s}^2[/tex].
The force on the ball will be
[tex]F_2=m_2a_2\\\Rightarrow F_2=5\times 24.5\\\Rightarrow F_2=122.5\ \text{N}[/tex]
The force on the ball is [tex]122.5\ \text{N}[/tex]
The reaction force on the skater will be equal to the force on the ball but will have opposite direction.
[tex]-F_1=F_2\\\Rightarrow -m_1a_1=F_2\\\Rightarrow a_1=-\dfrac{122.5}{56}\\\Rightarrow a_1=-2.1875\ \text{m/s}^2[/tex]
So, the skater will move towards left with a magnitude of acceleration [tex]2.1875\ \text{m/s}^2[/tex]
After the ball is thrown, the skater will accelerate to the left at 2.19 m/s² while the ball will accelerate to the right at 24.5 m/s².
The given parameters
The acceleration of the ball as it leaves the skaters hand is calculated as follows;
[tex]v^2 = u^2 + 2as\\\\ v^2 = 0 + 2as\\\\ a = \frac{v^2}{2s} \\\\ a = \frac{7^2}{2(1)} \\\\ a = 24.5 \ m/s^2[/tex]
The force experienced by the ball is calculated as follows;
[tex]F = ma\\\\ F_b = 5 \times 24.5\\\\ F_b = 122.5 \ N[/tex]
The force experienced by the skater is equal in magnitude to that of the ball but opposite in direction.
[tex]F_s = -F_b\\\\ F_s = -122.5 \ N[/tex]
The acceleration of the skater after the ball was thrown is calculated as follows;
[tex]F = ma \\\\ a = \frac{F}{m} \\\\ a = \frac{-122.5 }{56} \\\\ a =-2.19 \ m/s^2[/tex]
Thus, after the ball is thrown, the skater will accelerate to the left at 2.19 m/s² while the ball will accelerate to the right at 24.5 m/s².
Learn more about Newton's third law of motion here: https://brainly.com/question/25998091
