1. Understand the Problem
* Initial velocity: The stone is thrown upward with a speed of 15 m/s (positive since it's upward).
* Final position: The stone is caught 2.5 m above the starting point.
* Acceleration: Gravity acts on the stone, causing a downward acceleration of -9.8 m/s² (negative since it's downward).
* We need to find:
* Final velocity: How fast is the stone going when it's caught?
* Time: How long does it take to reach that point?
2. Apply the Relevant Equations
We'll use the following equations of motion:
* Equation 1: *v*² = *u*² + 2*a*s
* *v* = final velocity (what we want to find)
* *u* = initial velocity (15 m/s)
* *a* = acceleration due to gravity (-9.8 m/s²)
* *s* = displacement (2.5 m)
* Equation 2: *v* = *u* + *a*t
* *v* = final velocity (what we've found in Equation 1)
* *u* = initial velocity (15 m/s)
* *a* = acceleration due to gravity (-9.8 m/s²)
* *t* = time (what we want to find)
3. Calculate the Final Velocity
* Plug the values into Equation 1:
* *v*² = (15 m/s)² + 2 * (-9.8 m/s²) * (2.5 m)
* *v*² = 225 - 49 = 176
* *v* = √176 ≈ 13.3 m/s
4. Calculate the Time
* Plug the values (including the final velocity we just calculated) into Equation 2:
* 13.3 m/s = 15 m/s + (-9.8 m/s²) * *t*
* -1.7 m/s = (-9.8 m/s²) * *t*
* *t* = -1.7 m/s / (-9.8 m/s²) ≈ 0.17 s
Answer:
* The stone is going approximately 13.3 m/s when it's caught.
* It takes about 0.17 seconds to reach that point.
