A projectile of mass 0.451 kg is shot from a cannon, at height 7 m, as shown in the figure, with an initial velocity vi having a horizontal component of 4.9 m/s. The projectile rises to a maximum height of ∆y above the end of the cannon’s barrel and strikes the ground a horizontal distance ∆x past the end of the cannon’s barrel.Find the magnitude of the velocity vector when the projectile hits the ground. The acceleration of gravity is 9.8 m/s 2 . Answer in units of m/s.

To solve this problem, we need to find the magnitude of the velocity vector when the projectile hits the ground. We'll break the velocity into its horizontal and vertical components and find the final velocity at impact. Here's a step-by-step approach:

### Step 1: Horizontal motion
The horizontal velocity component remains constant throughout the motion because there is no horizontal acceleration (assuming no air resistance).

\[
v_{x} = 4.9 \, \text{m/s}
\]

### Step 2: Vertical motion
We know the projectile is launched from a height of 7 m and the acceleration due to gravity is \( g = 9.8 \, \text{m/s}^2 \).

Let's denote:
- Initial vertical velocity as \( v_{iy} \) (which is unknown),
- Final vertical velocity as \( v_{fy} \) (when the projectile strikes the ground),
- The height from which the projectile is launched as \( y_0 = 7 \, \text{m} \),
- Maximum height reached above the cannon as \( \Delta y \).

The projectile will rise to its maximum height, then fall back down. We use energy conservation to calculate the final vertical velocity. First, consider the following:

\[
v_{fy}^2 = v_{iy}^2 + 2g \Delta y
\]

Since the problem doesn't explicitly give \( v_{iy} \), we need to use a kinematic approach considering that the maximum height can also help us deduce more information. Would you like to provide a specific figure or clarification or

A projectile of mass 0.451 kg is shot from a cannon, at height 7 m, with an initial velocity having a horizontal component of 4.9 m/s. The projectile rises to a maximum height above the end of the cannon’s barrel and strikes the ground a horizontal distance past the end of the cannon’s barrel. Find the magnitude of the velocity vector when the projectile hits the ground. The acceleration of gravity is 9.8 m/s². Answer in units of m/s.

Find the magnitude of the velocity vector when a projectile is launched from a cannon at a height of 7 m, with a horizontal velocity of 4.9 m/s. Learn the key concepts of projectile motion, vertical and horizontal velocity components, and energy conservation. Suitable for students in Grades 10-12.

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