Mechanics (Part – 3)

If the angle is greater than 45°, the range will decrease and the height of the trajectory will increase.

When an object is projected into a vertical plane making an angle with the horizontal, its path is a parabola.

This motion of the body is called projectile motion.

Projectile motion is a type of motion in which an object is thrown from Earth's surface and moves in a Curved path under Gravitational force.

i.e. θ and (90-θ).

Velocity is a vector quantity, which means it contains a magnitude and a direction.

So can be changed either by changing the speed or by the velocity changing the direction of motion (or both).

Therefore, it may be possible that the speed is constant, but the velocity is changing because the direction is changing.

In this case, acceleration will be non-zero and equal to the rate of change in velocity.

     F=Δp/Δt  (P=mv)

If the projectile is launched at an angle $\theta$ with initial speed v, and assuming it lands at the same height:
                                                                       Total flight time = 2vsin⁡θ/g​

Where:

• v = initial velocity
• θ = angle of projection
• g= acceleration due to gravity (≈ 9.8 m/s²)

Whereas the weight varies according to the position of the object on the earth.

The weight of the object is maximum at the poles of the earth and minimum at the equator.

This change in weight occurs as a result of the shape of the earth and the rotation of the earth on its axis.

Momentum, P=mv

and

V=at

so we get P=m(at)

P=Ft    (∴F=ma)

since F is constant, momentum is the same for both bodies at the same time.

Later, Kepler formulated the laws of orbital motion of the planets.

                                                                        F= GM1M2 /r²

Here G is the gravitational constant.

Its value is 6.67×10⁻¹¹ Newton meter/kg².