A body is projected at some angle with a velocity of 100m/s and it takes 5 second to reach the ground. The change in its velocity for the whole motion is ........ [g=10 m/s2]

To determine the change in velocity for the entire motion of a projectile, we need to consider both the initial and final velocities of the body. In this case, the body is projected at a velocity of 100 m/s at some angle, and it takes 5 seconds to reach the ground. Let's break this down step by step.

Understanding Projectile Motion

When a body is projected at an angle, it follows a parabolic trajectory. The motion can be analyzed in two components: horizontal and vertical. The horizontal component of velocity remains constant (assuming no air resistance), while the vertical component changes due to gravity.

Initial Velocity Components

The initial velocity can be broken down into its horizontal (Vx) and vertical (Vy) components using trigonometric functions. However, since we are interested in the change in velocity for the whole motion, we can focus on the vertical component, as it will experience a change due to gravity.

Calculating Vertical Velocity Change

The vertical velocity at the moment of projection can be calculated as:

• Vy = V * sin(θ) (where θ is the angle of projection)

However, we don't need the angle to find the change in velocity. We know that the body takes 5 seconds to reach the ground. The final vertical velocity (Vy_final) just before it hits the ground can be calculated using the formula:

• Vy_final = Vy_initial + (g * t)

Here, g is the acceleration due to gravity (10 m/s²), and t is the time of flight (5 seconds).

Calculating Final Vertical Velocity

Assuming the vertical component of the initial velocity is Vy_initial, we can express the final vertical velocity as:

• Vy_final = Vy_initial + (10 m/s² * 5 s)
• Vy_final = Vy_initial + 50 m/s

Change in Velocity

The change in vertical velocity (ΔVy) during the entire motion can be expressed as:

• ΔVy = Vy_final - Vy_initial

Substituting the expression for Vy_final, we get:

• ΔVy = (Vy_initial + 50 m/s) - Vy_initial
• ΔVy = 50 m/s

Considering Horizontal Motion

For horizontal motion, the horizontal velocity (Vx) remains constant throughout the flight. Therefore, there is no change in horizontal velocity (ΔVx = 0).

Total Change in Velocity

Since the change in horizontal velocity is zero, the overall change in velocity for the entire motion is determined solely by the vertical component:

• ΔV_total = √(ΔVx² + ΔVy²)
• ΔV_total = √(0² + (50 m/s)²)
• ΔV_total = 50 m/s

Thus, the total change in velocity for the whole motion is 50 m/s. This reflects the increase in the downward velocity due to the acceleration from gravity during the time of flight.