First slide
The 3 equation for uniform acc
Question

When an object is shot from the bottom of a long smooth inclined plane kept at an angle 60° with horizontal, it can travel a distance x1 along the plane. But when the inclination is decreased to 30° and the same object is shot with the same velocity, it can travel x2 distance. Then, x1 : x2 will be

Moderate
Solution

The motion of the object shot in two cases can be depicted as below

Using third equation of motion,  v2 = u2 - 2gh      ......(i) 

As the object stops finally, so v = 0

For inclined motion, g = gsinθ and h = x

Substituting these values in Eq. (i), we get

  u2=2gsinθx

  x=u22gsinθ

For case I  x1=u22gsin600

For case II  x2=u22gsin300

  x1x2=u22gsin60°×2gsin30°u2

=12×23=13 or 1:3

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