Question

a particle is projected with a velocity 30 m/s at an angle theta with the horizontal , where theta=tan inverse [3/4].after 1 second , direction of motion of the particle makes an angle α with the horizontal then α is given by

Answer 1

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Suppose the velocities at both angles are u and v. Resolving u and v into horizontal and vertical components.

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Answer 2

Given :-

Initial velocity of particle = 30 ms-¹

Initial Angle of Projection = Ø = tan-¹(3/4)

Acceleration due to gravity = g = 10 ms-².

After 1 s, particle makes an angle α with the horizontal.

To find : - Value of α.

Horizontal Velocity = ux = u CosØ = 24 ms-¹.

Vertical Velocity = uy = u SinØ = 18 ms-¹.

After 1 s,

Horizontal Velocity will be same, but Vertical Velocity will change,

-uy = -gt

uy = 10 × 1

uy = 10 ms-¹

∆uy = (18 - 10) ms-¹ = 8 ms-¹

Again,

tan α = uy/ux

tan α = 8/24

tan α = 1/3

α = tan-¹(1/3)

Hence,

Final angle of Projection = α = tan-¹(1/3).