A cart rolls with negligible friction on a ramp that is inclined at an 17 degree

Question

A cart rolls with negligible friction on a ramp that is inclined at an 17 degree angle above level ground. It is released from rest and reaches the bottom of the ramp in 4 seconds. How far did it travel along the ramp? What was the vertical height from which the cart was released? At the bottom of the first ramp, the cart smoothly rolls onto a second ramp without losing any significant amount of speed. The second ramp is tilted up above the ground by an angle of 20 degrees. What distance up the ramp does the cart reach before coming to rest (give the distance as measured from the base of the second ramp)? What is the maximum vertical height that the cart reaches when it rolls up the second ramp?

Explanation / Answer

Acceleration along the ramp = g * sin x = 9.8*sin(17 degree)=2.87m/s

1)So distance travlled along ramp = 1/2*a*t^2=1/2*2.87*4^2=22.96m

2)Vertical height = distance along ramp * sin x = 22.96*sin(17 degree)=6.71m

3)The vertical height reached would be same because potential energy only depends on vertical height.

So distance travelled along second ramp = 6.71/sin(20 degree)=19.61m

4)The maximum vertical height remains same and is 6.71 m

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