A coin is projected from earth's surface with velocity of 50 ms-1. What is the angle of projection after 2 seconds, it reaches a wall of 5 m high

To determine the angle of projection of a coin that is launched from the Earth's surface with an initial velocity of 50 m/s and reaches a wall 5 meters high after 2 seconds, we can break down the problem using the principles of projectile motion. Let's analyze the situation step by step.

Understanding Projectile Motion

Projectile motion involves two components: horizontal and vertical. The initial velocity can be broken down into these two components based on the angle of projection, which we will denote as θ. The equations governing the motion will help us find the angle.

Key Equations

For projectile motion, the following equations are crucial:

• Vertical displacement: y = v₀y * t - 0.5 * g * t²
• Horizontal displacement: x = v₀x * t

Where:

• y is the vertical displacement (5 m in this case).
• v₀y is the initial vertical velocity component.
• g is the acceleration due to gravity (approximately 9.81 m/s²).
• t is the time of flight (2 seconds).

Breaking Down the Initial Velocity

The initial velocity (v₀) can be split into its vertical and horizontal components:

• v₀y = v₀ * sin(θ)
• v₀x = v₀ * cos(θ)

Given that the total initial velocity is 50 m/s, we can express these components as:

• v₀y = 50 * sin(θ)
• v₀x = 50 * cos(θ)

Calculating Vertical Displacement

Now, substituting the values into the vertical displacement equation:

5 = (50 * sin(θ)) * 2 - 0.5 * 9.81 * (2)²

Let's simplify this:

5 = 100 * sin(θ) - 0.5 * 9.81 * 4

5 = 100 * sin(θ) - 19.62

Now, rearranging gives us:

100 * sin(θ) = 5 + 19.62

100 * sin(θ) = 24.62

Thus, we find:

sin(θ) = 24.62 / 100

sin(θ) = 0.2462

Finding the Angle of Projection

To find the angle θ, we take the inverse sine:

θ = arcsin(0.2462)

Using a calculator, we find:

θ ≈ 14.3 degrees

Final Thoughts

So, the angle of projection required for the coin to reach a wall 5 meters high after 2 seconds, given an initial velocity of 50 m/s, is approximately 14.3 degrees. This example illustrates how projectile motion can be analyzed using basic physics principles, allowing us to solve for unknowns like the angle of projection.