Projectile On An Inclined Plane

Question

A particle is projected with speed 20 m/s horizontally from the top of an incline that makes 30 degrees with the horizontal, directed down the slope. Taking g = 10 m/s^2, after what time does the particle strike the inclined surface?

RankGuru · Accepted Answer

Projectile motion onto an incline is best handled by writing the horizontal and vertical displacements separately and imposing the geometric constraint that the landing point must lie on the sloping surface. Taking the launch point as origin with $x$ measured horizontally and $y$ measured vertically downward, the horizontal displacement is $x = ut = 20t$ and the vertical drop under gravity is $y = 	frac{1}{2}gt^2 = 5t^2$. Because the incline descends at 30 degrees below the horizontal, any point on its surface satisfies $	an 30^\circ = \frac{y}{x}$, equating the ratio of vertical drop to horizontal run with the tangent of the slope angle. Substituting gives $\frac{5t^2}{20t} = \frac{1}{\sqrt{3}}$, which simplifies to $\frac{t}{4} = \frac{1}{\sqrt{3}}$, so $t = \frac{4}{\sqrt{3}}	ext{ s} \approx 2.31	ext{ s}$. The option $\frac{2}{\sqrt{3}}$ s halves the correct root by misplacing the factor of four from the displacement ratio. The option $\sqrt{3}$ s ignores the launch speed entirely. The option 2 s assumes a 45-degree slope rather than 30 degrees. This is the standard JEE Advanced slope-constraint method for projectiles. As a check, a gentler 30-degree incline lets the particle travel farther before meeting the surface, so a flight time above two seconds is physically reasonable.

Projectile On An Inclined Plane

Select the correct option:

🔒 Solution Hidden from View

More kinematics Practice Questions

A body starting from rest moves with uniform acceleration of 6 m/s² along a straight road, what dist...

A javelin is launched at 40 m/s at 45 degrees to the horizontal across a level field, with g equal t...

A particle is said to be in uniform motion along a straight line when which of the following conditi...

A ball thrown vertically upward with an initial speed of 20 m/s reaches its highest point, taking g ...

From the top of a building a ball is dropped just as another ball is thrown up from the ground at 25...

A particle moves 8 m east and then 6 m north in a total time of 5 seconds along a flat surface, what...

Among the following physical quantities encountered in motion, which one is correctly classified as ...

The position of a particle along a straight line varies with time as x equals 2t cubed minus 3t squa...

A swimmer who can swim at 4 m/s in still water heads straight across a river flowing at 3 m/s, what ...

A motorcyclist moving at 30 m/s applies brakes and decelerates uniformly at 5 m/s², how far does the...

On a velocity-time graph, a body moves with velocity increasing uniformly from 5 m/s to 25 m/s over ...

The slope of a position-time graph at any instant for a moving particle physically represents which ...

About This Question

Solution