What is the relationship between time of flight T and horizontal range r?

R=2tanθgT2​

What is the relation between R and H in projectile motion?

Hint: R, the horizontal range of a projectile is the total horizontal distance that travels in a motion. And H is the maximum height a body attains in a projectile before it starts to fall downwards.

What is the formula for angle of projection?

(1) where U is the initial velocity, θ is the angle of projection and g is the acceleration due to gravity. The horizontal distance covered by the projectile i.e. range is given by, R=U2Sin2 θ g… (2).

What is the relationship between the angle of the projectile and its range?

As it rises and falls, air resistance has a negligible effect. The distance traveled horizontally from the launch position to the landing position is known as the range. The range of an angled-launch projectile depends upon the launch speed and the launch angle (angle between the launch direction and the horizontal).

How does the angle of projection affect the range and height of a projectile?

Just like the case of the time of flight, we see that maximum height reached by the projectile depends on both initial speed and the angle of projection (θ). Greater the initial velocity and greater the angle of projection from horizontal direction, greater is the height attained by the projectile.

What is angle of projection of projectile?

(i) Angle of projection – It is the angle with the surface with which the projectile is projected. The maximum range angle of the projectile should be 450.

What is the best angle of projection for a projectile to reach the longest range Why?

45 degrees
A projectile, in other words, travels the farthest when it is launched at an angle of 45 degrees.

What is the best angle of projection for a projectile to reach the longest range?

What is the maximum range of a projectile at 45 degrees?

As the angle of projection is always acute it can take only + 1 value. Thus for a given velocity of projection, the horizontal range is maximum when the angle of projection is 45°. Thus, for a given velocity of a projection, the maximum range of a projectile is 4 times the maximum height reached by it.

Why does the range of projectile vary with the quantity ‘sin2θ’?

The component v 0 cos θ causes the horizontal displacement of the body. In this case, the velocity of projection v 0, the acceleration due to gravity ‘g’ is constant. Hence the range of projectile varies directly with the quantity ‘Sin 2θ’. The range is maximum when the value of the quantity ‘Sin 2θ’ is maximum.

What is the horizontal distance travelled by a projectile called?

The horizontal distance travelled by a projectile is called its range. A projectile launched on level ground with an initial speed v0 at an angle θ above the horizontal will have the same range as a projectile launched with an initial speed v0 at 90° − θ and maximum range when θ = 45°. (1 vote)

How do two complementary angles of projections give the same range?

Thus, for a given velocity of a projection, the maximum range of a projectile is 4 times the maximum height reached by it. To Show that two complementary angles of projections give the same range of the projectile. Le θ and (90° – θ) be the two complementary angles of projections. The range in two cases is given by