what minimum speed does a 100g puck need to make it to the top of a 3m long 20degree frictionless ramp?

mgh=1/2mv^2

To find h

sin 20= h/3
Put h and g in above equation and you are happpy :)

Enough speed such that the initial kinetic energy (1/2)MV^2, equals the potential energy gain at maximum elevation, M g H.

M cancels out, so you don't need to know the mass. You DO need to calculate H. Use trigonometry.

This sucked, terrible explanation

To find the minimum speed a 100g puck needs to make it to the top of a 3m long 20-degree frictionless ramp, we can use the principles of energy conservation.

Let's break down the problem into two parts:

1. Vertical Component: The weight of the puck is acting vertically downward and we need to overcome it to reach the top of the ramp.
2. Horizontal Component: The horizontal component of the velocity will enable the puck to cover the 3m distance along the ramp.

First, let's calculate the height the puck needs to reach at the top of the ramp. Using trigonometry, we can determine the vertical displacement (h) as follows:

h = sin(20°) * 3m

Next, we can find the gravitational potential energy (PE) of the puck at the top of the ramp using its mass (m = 100g) and the gravitational acceleration (g = 9.8 m/s^2):

PE = m * g * h

Now, the puck needs to have a certain amount of kinetic energy (KE) at the bottom of the ramp to reach the height h. The KE is given by:

KE = (1/2) * m * v^2

Where v is the minimum speed of the puck required.

Since energy is conserved, we can equate the potential energy at the top of the ramp (PE) with the kinetic energy at the bottom (KE):

PE = KE

m * g * h = (1/2) * m * v^2

By canceling out the mass (m) from both sides, we get:

g * h = (1/2) * v^2

Now, we can solve for v by rearranging the equation:

v^2 = 2 * g * h

v = sqrt(2 * g * h)

Substituting the values, we have:

v = sqrt(2 * 9.8 m/s^2 * sin(20°) * 3m)

Calculating this expression, we find:

v ≈ 7.04 m/s

Therefore, the minimum speed the 100g puck needs is approximately 7.04 m/s to make it to the top of a 3m long 20-degree frictionless ramp.