Grade 12Mechanics

A particle is projected from a horizontal floor with speed 10m/s at an angle 30 degrees with the floor and striking the floor after sometime.
Q1)What will be the minimum speed of particle ?
Q2) What will be the displacement of particle after half second?

Riya Das

7 Years agoGrade 12

1 Answer

Samyak Jain

7 Years ago

When particle is projected, magnitude of horizontal component of velocity is u_x = 10 cos30 = 10 $\sqrt{3}$ / 2 = 5 $\sqrt{3}$ m/s and that of vertical component is u_y = 10sin30 10.1/2 = 5 m/s.

Horizontal component of velocity is constant, while magnitude of vertical velocity is varying with time.

Minimum speed of particle means minimum vertical velocity which is zero.

So, minimum speed of particle is 5 $\sqrt{3}$ m/s.

For displacement of particle after half second, consider horizontal displacement x and vertical displacement y separately.

x = u_x t = 5 $\sqrt{3}$ . 1/2 = 5 $\sqrt{3}$ / 2 m/s = 10 $\sqrt{3}$ / 4 m/s and

y = u_yt – (1/2) g t² = 5.1/2 – (1/2).10.1/4 = 5/2 – 5/4 = 5/4.

Magnitude of displacement of the particle after half second = $\sqrt{x^2 + y^2}$ = $\sqrt{(10\sqrt{3}/4)^2 + (5/4)^2}$

= (1/4) $\sqrt{325}$ $\approx$ (1/4) . (18.028) = 4.507 m

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A particle is projected from a horizontal floor with speed 10m/s at an angle 30 degrees with the floor and striking the floor after sometime. Q1)What will be the minimum speed of particle ?Q2) What will be the displacement of particle after half second?

Riya Das

1 Answer

Samyak Jain

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A particle is projected from a horizontal floor with speed 10m/s at an angle 30 degrees with the floor and striking the floor after sometime.
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