An arrow is shot horizontally from a height of 4.9 m above the ground. The initial speed of the arrow is 45 m/s. Neglecting friction, how long will it take the arrow to hit the ground?

Options

A. 9.2 s
B. 1.0 s
C. 6.0 s
D. 1.4 s

Answer

To solve the problem of how long it will take for an arrow shot horizontally from a height of 4.9 m to hit the ground, we can follow these steps:

### Step 1: Identify the given information
- Height (h) = 4.9 m
- Initial horizontal speed (u) = 45 m/s (this value will not affect the time to hit the ground)
- Acceleration due to gravity (g) = 9.8 m/s² (acting downwards)

### Step 2: Use the kinematic equation for vertical motion
Since the arrow is shot horizontally, its initial vertical velocity (u_y) is 0 m/s. We can use the following kinematic equation for vertical motion to find the time (t) it takes to hit the ground:

\[ h = u_y t + \frac{1}{2} g t^2 \]

Substituting the known values into the equation:

\[ 4.9 = 0 \cdot t + \frac{1}{2} \cdot 9.8 \cdot t^2 \]

This simplifies to:

\[ 4.9 = 4.9 t^2 \]

### Step 3: Solve for time (t)
Now, we can divide both sides of the equation by 4.9:

\[ 1 = t^2 \]

Taking the square root of both sides gives:

\[ t = \sqrt{1} \]

Thus,

\[ t = 1 \text{ second} \]

### Conclusion
The time it takes for the arrow to hit the ground is **1 second**.

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