How Fast Will Zeke Slide Down the Hill?

[batman617]

Homework Statement

Zeke begins to slide down a snow hill on a rubber mat. Zeke's mass is 76 kg and that of the mat is 2kg.

Homework Equations

Disregarding frictional forces, how fast are they moving when they are 1.2 m below the crest?

The Attempt at a Solution

v=(square root)2gh
v=(square root)(2)(9.8)(-1.2)
v=4.85 m/s

I don't think this is even close to being right, as a friend who I just got done talking to (and is 10x smarter than me) said he got a completely different answer.

By the way, hello everyone! I just signed up, hoping to learn to understand physics better.

 

[Shooting Star]

Hello, we do hope you understand better from now on.

Does the problem mention 1.2 m vertically below the crest or 1.2 m along the slope?

If it's the first case, your eqn is correct, except for the minus sign under the sqrt. Is that possible?

If it's the second case, you'll have to take the component of g along the slope.

 

[Moetasim]

I love the subject but I'm not that great at it.

Hello! I would approach this problem by first defining the variables and assumptions. The mass of Zeke and the mat are given, but we also need to consider the acceleration due to gravity (g), which is assumed to be 9.8 m/s^2. We are also disregarding frictional forces, which means that the only force acting on Zeke and the mat is the force of gravity.

Next, we can use the equation for gravitational potential energy (PE = mgh) to find the initial potential energy of Zeke and the mat at the top of the hill. This can then be converted into kinetic energy (KE = 1/2mv^2) as they slide down the hill.

Using conservation of energy, we can equate the initial potential energy to the final kinetic energy. This will give us the final velocity (v) at 1.2 m below the crest.

So, the equation would be: mgh = 1/2mv^2

76 kg * 9.8 m/s^2 * 1.2 m = 1/2 * (76 kg + 2 kg) * v^2

v = 4.89 m/s

This is slightly different from your friend's answer, but it is within a reasonable range. It's always good to check your calculations and assumptions to make sure you're on the right track. I hope this helps!