Question

A projectile is fired with an initial velocity of 200 m/s to hit a target located

500 m above the level of gun point and at a horizontal distance of 300 m.

Neglecting the air resistance, determine the angle of projection of the

projectile.​

Answer 1

Answer:

Explanation:

Let us consider a ball projected at an angle θ with respect to horizontal x-axis with the initial velocity u .

The point O is called the point of projection, θ is the angle of projection and OB = horizontal range. The total time taken by the particle from reaching O to B is called the time of flight.

Now,

(a). The total time of flight is

Resultant displacement is zero in Vertical direction.

Therefore, by using equation of motion

s=ut−

2

1

​

gt

2

gt=2sinθ

t=

g

2sinθ

​

(b). The horizontal range is

Horizontal range OA = horizontal component of velocity × total flight time

R=ucosθ×

g

2usinθ

​

R=

g

u

2

sin2θ

​

(c). The maximum height is

It is the highest point of the trajectory point A. When the ball is at point A, the vertical component of the velocity will be zero.

By using equation of motion

v

2

=u

2

−2as

0=u

2

sin

2

θ−2gH

H=

2g

u

2

sin

2

θ

​