Question

Two frisky otters slide down frictionless hillsides of the same height but different slopes. The slope of the hill of otter 1 is 30 degrees, while the slope of the hill of otter 2 is 60 degrees. If both start from rest, which otter is moving faster when she reaches the bottom of her hill

Answer 1

Answer:

The  frisky otters will be moving at the same speed  at the bottom of the hill because the hillsides are of the same height

Explanation:

From the question we are told that

   The slope of the hill of otter one is $\theta_1 = 30^o$

   The slope of the hill of otter two  is  $\theta _2 = 60^o$

Generally the from the law of energy conservation

     $PE_{top} = KE_{bottom}$

Here  $PE_{top} = mgh$

and  $KE_{bottom} = \frac{1}{2} mv^2$

So

       $mgh = \frac{1}{2} m v^2$

=>   $v = \sqrt{2gh}$

From this equation for v we see that velocity is only dependent on the height and is not affected by the slope

Hence both frisky otters will travel at same speed because the hillsides are of the same height

Answer 2

just wanted to say that the other person is correct, my computer lagged and i gave them one star :(