How Does Angle Affect Speed and Distance of a Toy Car on a Ramp?

[lovemake1]

Homework Statement

The toy car has been placed on an inclied ramp facing downward. angles are as follows 10degrees , 12 degrees , 14 degrees , 16degrees , 18 degrees, 20 degrees.

after acceleratin down the ramp for 15cm, the car continues on a leveled plane.
between which consecutive angles will show a big difference in their speed and distance traveled.

Homework Equations

Fnet = ma
Fgx - Ff = ma

vf ^2 = vi ^2 + 2ad

The Attempt at a Solution

my prediction is that there will be biggere difference in 12 and 14 degree angles because the
car hasnt put to its full potential yet and at low angles like this one, it is easier to see the performance increase.
or would it be the other way around 16 degree angle and 18 degree angle?
i know that as the angles increase the x-component of the gravitational force increases more than the frictional force which is the reason why the car travels further and further.

can someone please help with this concept Help !

 

[ideasrule]

Derive an equation for the speed and for the distance traveled as a function of theta. Then decide what the answer should be based on those.

 

[lovemake1]

what do you mean as a function of theta?

Fgx - Ff = ma
mg (sin theta - coeff of static friction ) = ma
g (sin theta - coeff of static friction ) = a


vf ^2 = vi ^2 + 2ad
0 = vi^2 + 2(g(sin theta - coeff of static friction))d

and solve for d? , is this what you mean by function of theta? I am don't understand
Help