What minimum speed does a 100 g puck need to make it to the top of a 4.60 m -long, 24.0 ∘ frictionless ramp?

The minimum speed that a 100 g puck needs to make it to the top of a 4.60 m -long, 24.0 ∘ frictionless ramp is 6.05m/s

The kinetic energy along the ramp is equal to the potential energy at the top.

KE = PE

Given the following parameters

g is the acceleration due to gravity = 9.8m/s²

h = 4.60sin24⁰

h = 1.870m

Get the minimum speed required

Hence the minimum speed that a 100 g puck needs to make it to the top of a 4.60 m -long, 24.0 ∘ frictionless ramp is 6.05m/s

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6.05 m/s

Explanation:

In order for the puck to reach the top of the ramp, its initial kinetic energy must be equal to its final potential energy.

So we can write:

(1)

where

m = 100 g = 0.1 kg is the mass of the puck

v is the initial speed of the puck

is the acceleration due to gravity

h is the height of the ramp

Here we know that

d = 4.60 m is the length of the ramp

is the angle of the ramp

So its height is

So now we can re-arrange eq (1) to find the minimum speed of the puck: