Certainly! Let's solve the problem step by step.
### Given:
1. Initial velocity ([tex]\( v \)[/tex]) = [tex]\( 12.25 \, \text{m/s} \)[/tex]
2. Time of flight ([tex]\( t \)[/tex]) = [tex]\( 2.5 \, \text{s} \)[/tex]
### To find:
Horizontal displacement ([tex]\( d \)[/tex])
### Concept:
When a projectile is thrown, its horizontal displacement is determined by its horizontal velocity and the time of flight. Since there is no horizontal acceleration (assuming negligible air resistance), the horizontal velocity remains constant throughout the flight.
The horizontal displacement can be calculated using the formula:
[tex]\[ d = v \times t \][/tex]
### Solution:
1. Identify the horizontal velocity, which in this case is [tex]\( 12.25 \, \text{m/s} \)[/tex].
2. Identify the time of flight, which is [tex]\( 2.5 \, \text{s} \)[/tex].
3. Substitute the known values into the formula:
[tex]\[
d = 12.25 \, \text{m/s} \times 2.5 \, \text{s}
\][/tex]
4. Multiply the values:
[tex]\[
d = 30.625 \, \text{m}
\][/tex]
### Conclusion:
The horizontal displacement of the projectile is [tex]\( 30.625 \, \text{m} \)[/tex].
