# Calculating the initial speed of an object that decelerates in a ramp.

**1. The problem statement, all variables and given/known data**

Hello,

An object moves at constant speed in a horizontal surface. Suddenly, a ramp comes along its way. The object starts to climb such ramp. Due to this, the object starts to lose speed. At certain distance, the object loses all of its speed. I want to calculate the value of the objects speed just before entering the ramp. Suppose that I know the value of the distance that the object travels on the ramp before stopping, the value of the coefficient of friction between the object and the ramp, the angle of elevation of the ramp and the value of acceleration due to gravity. I know that the following equation works for objects that decelerate in horizontal surfaces: velocity= the square root of: 2*distance*coefficient of friction*acceleration of gravity.

But, if the object decelerates in an elevated ramp, should I include trigonometry in the equation? I mean: should I multiply cos of the angle of elevation of the ramp, or sin or tan in the equation?

**2. Relevant equations**

velocity= the square root of: 2*distance*coefficient of friction*acceleration of gravity ¿(*tan, *sin, *cos)?

**3. The attempt at a solution**

It makes sense to me that trigonometric functions should be included inside the equation because the normal force of the object is altered due to the slope. But, if this is true, I have no idea which function to include and why. Thanks a lot!

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