Question

How would you solve this?

1/2 mv^2 - 1/2 m x 25 = mg x 100sin20

I obtained this from the question:

A girl on a sledge starts, with a speed of 5 m/s, at the top of a slope of length 100 m which is at an angle of 20 degrees to the horizontal. The sledge slides directly down the slope. Given that there is no resistance to the sledge's motion, find the speed of the sledge at the bottom of the slope.

g=10

Thanks for the help!

Answer 1

solve for v! m divides out...
v^2=2*g*100sin20+25
then take square root of each side.

Answer 2

1/2 m V^2 = 1/2 m v^2 + m g h

cancel the m's , solve for V
... or v in your equation

algebra time

Answer 3

Brace yourself for some potentially potent facepalming, because I haven't quite gotten the hang of it so I'm gonna let you helpful Jiskhans in on my dimwittedness!

Starting with 1/2 m v^2 - 1/2 m 25 = m g 100sin20, you bring the -1/2 m 25 over to the other side, giving:
1/2 m v^2 = 1/2 m 25 + mg 100sin20

Then I add the two things on the right:
1/2 m v^2 = 354.5m <-- Then I cancel the m's and square root to give:
v= 26.6 m/s

Does this look correct? Thanks for checking!

Answer 4

h = 100*sin20 = 34.2 m.

V^2 = Vo^2 + 2g*h.
V^2 = 5^2 + 20*34.2 = 709,
V = 26.63 m/s.