a 65 kg student, starting from rest , slides down an 8 meter high water slide. how fast is he going at the bottom of the slide ?
To find the speed at the bottom of the slide, we can use the principle of conservation of energy.
Step 1: Calculate the potential energy at the top of the slide:
Potential energy (PE) = mass (m) × acceleration due to gravity (g) × height (h)
PE = 65 kg × 9.8 m/s^2 × 8 m
Step 2: Calculate the kinetic energy at the bottom of the slide:
Since the student starts from rest, the initial kinetic energy is zero.
At the bottom of the slide, all the potential energy will be converted into kinetic energy.
Kinetic energy (KE) = Potential energy (PE) at the top of the slide
Step 3: Calculate the speed using kinetic energy formula:
Kinetic energy (KE) = (1/2) × mass (m) × velocity (v)^2
Setting the potential energy equal to the kinetic energy:
65 kg × 9.8 m/s^2 × 8 m = (1/2) × 65 kg × v^2
Simplifying the equation:
5096 = 32.5 × v^2
Divide both sides by 32.5:
v^2 = 5096 / 32.5
v^2 = 156.9231
Take the square root of both sides:
v = √156.9231
v ≈ 12.5174 m/s
Therefore, the student is going approximately 12.5 m/s at the bottom of the slide.
To find out the speed at the bottom of the slide, we can apply the principle of conservation of energy. The initial potential energy at the top of the slide is converted into kinetic energy at the bottom.
Here's how to calculate it:
1. Determine the potential energy at the top of the slide using the formula: Potential Energy (PE) = mass (m) × gravitational acceleration (g) × height (h).
PE = 65 kg × 9.8 m/s² × 8 m
PE = 5,072 Joules
2. Apply the principle of conservation of energy, which states that the total energy at the top of the slide (potential energy) is equal to the total energy at the bottom of the slide (kinetic energy).
PE = Kinetic Energy (KE)
KE = 5,072 Joules
3. Use the formula for kinetic energy: KE = 0.5 × mass × velocity².
5,072 Joules = 0.5 × 65 kg × velocity²
4. Rearrange the formula to solve for velocity:
velocity² = (2 × KE) / m
velocity² = (2 × 5,072 Joules) / 65 kg
velocity² = 155.58 m²/s²
5. Take the square root of both sides to find the velocity:
velocity = √(155.58 m²/s²)
velocity ≈ 12.48 m/s
Therefore, the student is going approximately 12.48 m/s at the bottom of the slide.
V^2 = Vo^2 + 2g.h.
V^2 = 0 + 19.6*8 = 156.8
V = 12.5 m/s.