Calculate Time: 500 km/h Projectile Covering 150 Meters

To solve this problem, we'll follow these steps:

• Step 1: Convert the speed from km/h to m/s.
• Step 2: Apply the formula for time.
• Step 3: Calculate the time taken using the formula.

Now, let's work through each step:

Step 1: Convert the speed from km/h to m/s
The speed is given as 500 km/h. We know that 1 km/h is equal to $\frac{1000}{3600}$ m/s (since there are 1000 meters in a kilometer and 3600 seconds in an hour). Thus, we have:

$500 \, \text{km/h} = 500 \times \frac{1000}{3600} \, \text{m/s} = \frac{500 \times 1000}{3600} \, \text{m/s}$

$= \frac{500000}{3600} \, \text{m/s} \approx 138.89 \, \text{m/s}$

Step 2: Apply the formula for time
Using the formula $t = \frac{d}{v}$, where $d = 150 \, \text{meters}$ and $v = 138.89 \, \text{m/s}$, we calculate the time:

$t = \frac{150}{138.89}$

Step 3: Calculate the time:
Perform the calculation:

$t \approx 1.08 \, \text{seconds}$

Therefore, the solution to the problem is $1.08$ seconds.