A particle at a height h from the ground is projected with an angle 300 from the horizontal, it strikes the ground making an angle 450with horizontal. It is again projected from the same point with the same speed but with an angle of 600 with horizontal. Find the angle it makes with the horizontal when is strikes the ground. a)tan-1(5) b)tan-1(root5) c)tan-1(3) d)tan-1(root3)?

Question

Answer

Answer

To solve this problem, we can use the laws of projectile motion. Let's break down the problem into two parts:

Part 1: Projectile motion with an angle of 30°
- The particle is projected at an angle of 30° from the horizontal.
- It strikes the ground at an angle of 45° with the horizontal.
- We need to find the angle it makes with the horizontal when it strikes the ground.

Let's assume the initial velocity of the particle is v m/s. We can break down this velocity into its horizontal (v*cosθ) and vertical (v*sinθ) components.

Using the equation of motion, we can find the time taken by the particle to reach the ground:
h = (v*sinθ)t - (0.5*g*t^2)
Here, h is the height, θ is the angle, g is the acceleration due to gravity, and t is the time taken.

Since the particle strikes the ground at an angle of 45°, the horizontal component of velocity remains the same (v*cosθ). The vertical component of velocity becomes zero.

Using the equation of motion for vertical motion, we can find the time of flight:
0 = (v*sinθ) - (g*t)
Solving these two equations, we can find the time taken by the particle to reach the ground.

Now, we can find the horizontal distance traveled by the particle:
Horizontal distance = (v*cosθ) * time

Part 2: Projectile motion with an angle of 60°
- The particle is projected again from the same point with the same speed but at an angle of 60° from the horizontal.
- We need to find the angle it makes with the horizontal when it strikes the ground.

Using the same approach as in Part 1, we can find the time taken by the particle to reach the ground and the horizontal distance traveled.

Finally, we can find the angle made by the particle with the horizontal when it strikes the ground:
tan(θ') = (vertical distance) / (horizontal distance)
Here, θ' is the angle made by the particle with the horizontal when it strikes the ground.

We can substitute the values of the vertical distance and horizontal distance into this equation to find the angle θ'. The correct option from the given choices can be determined by evaluating the tangent inverse of the ratio.

Therefore, the answer is option d) tan-1(root3).

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