Final answer:
By using the conservation of energy principle, we equate the potential energy at the top of the slide with the kinetic energy at the bottom. This calculation shows that the swimmer's velocity at the bottom of the slide will be 6.26 m/s.
Step-by-step explanation:
To calculate the velocity of the swimmer at the bottom of the slide, we can use the principles of conservation of energy. Specifically, we can equate the potential energy at the top of the slide to the kinetic energy at the bottom of the slide, assuming there is no significant energy loss due to friction or air resistance.
At the top of the slide, the swimmer's potential energy (PE) is given by the equation:
PE = m × g × h
Where:
- m is the mass of the swimmer (60 kg)
- g is the acceleration due to gravity (9.81 m/s2)
- h is the height of the slide (2 m)
At the bottom of the slide, all of this potential energy has been converted to kinetic energy (KE), which is given by the equation:
KE = 0.5 × m × v²
Setting the potential energy equal to the kinetic energy and solving for v, the velocity, we get:
m × g × h = 0.5 × m × v²
Now, we can cancel m from both sides as it appears in both the potential and kinetic energy equations:
g × h = 0.5 × v²
Finally, we solve for v:
v = √(2 × g × h)
Filling in the values:
v = √(2 × 9.81 m/s2 × 2 m)
The swimmer's velocity at the bottom of the slide is 6.26 m/s.