A 0.09 kg marble sits at rest on the top of a sloping, frictionless track. a. If the slope has a height of 1.5 m, calculate the velocity of the marble at the bottom of
the slope.

Explanation:

Notice that nothing but the mass and height are given, and the mass is not really necessary. It will cancel when we do the problem.

So the potential energy at the top equals the Kinetic energy at the bottom.

PE_top = Ke_bottom

mgh = 1/2 m v^2          Divide by m

mgh/m =1/2 mv^2/m

gh = 1/2 v^2                  Multiply both sides by 2

2gh = v^2                    

Givens

g = 9.81

h = 1.5

Solution

2*9.81 * 1.5 = v^2

29.43 = v^2

v = sqrt(29.43)

v = 5.425

the answer is a. the yacht traveled from the dock north to the 200-meter marker in the bay in less than 5 minutes, giving the passengers several more hours to fish.

im doing peak rn so sry if its wrong

one "light year" is the distance that light travels, through vacuum, in one julian year.   that's 365.25 days, of 24 hours each.