Answer:
It takes 21.7 seconds for Skid to reach the edge of the pond.
Explanation:
We can calculate the time that takes Skid to reach the edge of the pond by conservation of linear momentum:
[tex] p_{i} = p_{f} [/tex]
[tex] m_{1}v_{1_{i}} + m_{2}v_{2_{i}} = m_{1}v_{1_{f}} - m_{2}v_{2_{f}} [/tex] (1)
Where:
m₁: is the Skid's mass
m₂: is the book's mass = 2.6 kg
[tex]v_{1_{i}}[/tex]: is the initial speed of Skid = 0 (he was at rest)
[tex]v_{2_{i}}[/tex]: is the initial speed of the book = 0 (it was at rest)
[tex]v_{1_{f}}[/tex]: is the final speed of Skid =?
[tex]v_{2_{f}}[/tex]: is the final speed of the book = 4 m/s. This value is negative since it is moving in the opposite direction of Skid.
First, we need to calculate Skid's mass.
[tex] m_{1} = \frac{P}{g} [/tex]
Where:
P: is the weight of Skid = 440 N
g: is the acceleration due to gravity = 9.81 m/s²
[tex] m_{1} = \frac{P}{g} =\frac{440 N}{9.81 m/s^{2}} = 44.8 kg [/tex]
Now, we can find the speed of Skid from equation (1):
[tex] 0 = 44.8 kg*v_{1_{f}} - 2.6 kg*4 m/s [/tex]
[tex] v_{1_{f}} = \frac{2.6 kg*4 m/s}{44.8 kg} = 0.23 m/s [/tex]
Finally, the time to reach the edge can be found by using the following equation:
[tex] v_{1_{f}} = \frac{d}{t} [/tex]
Where:
d: is the distance = radius = 5 m
t: is the time =?
[tex] t = \frac{d}{v_{1_{f}}} = \frac{5 m}{0.23 m/s} = 21.7 s [/tex]
Therefore, it takes 21.7 seconds for Skid to reach the edge of the pond.
I hope it helps you!
