A projectile fired from a gun has initial horizontal and vertical components of velocity equal to 30 m/s and 40 m/s, respectively.
Approximately how long does it take the projectile to reach the highest point in its trajectory?

Options

A. 1 s
B. 4 s
C. 2 s
D. 8 s

Answer

To find the time it takes for the projectile to reach the highest point in its trajectory, we can follow these steps:

### Step 1: Understand the Components of Motion
The projectile has two components of velocity:
- Horizontal component (u_x) = 30 m/s
- Vertical component (u_y) = 40 m/s

### Step 2: Identify the Relevant Formula
The time to reach the highest point (t) can be calculated using the formula:
\[ t = \frac{u_y}{g} \]
where:
- \( u_y \) is the initial vertical component of velocity,
- \( g \) is the acceleration due to gravity.

### Step 3: Use the Value of g
For this problem, we can use \( g \approx 10 \, \text{m/s}^2 \) for simplicity (as suggested in the video).

### Step 4: Substitute the Values
Now we can substitute the values into the formula:
\[ t = \frac{40 \, \text{m/s}}{10 \, \text{m/s}^2} \]

### Step 5: Calculate the Time
Calculating the above expression gives:
\[ t = 4 \, \text{seconds} \]

### Conclusion
Thus, the time taken for the projectile to reach the highest point in its trajectory is approximately **4 seconds**.

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