You are standing on the roof of a building 300 m high, and throw a stone upward at 25 m/s. Find the speed of the stone as it strikes the ground.
To find the speed of the stone as it strikes the ground, we can use the equations of motion.
First, let's find the time it takes for the stone to reach its maximum height:
1. The initial velocity (u) of the stone is +25 m/s (upward).
2. The acceleration (a) due to gravity is -9.8 m/s^2 (downward).
3. The final velocity (v) at the top of the trajectory is 0 m/s.
We can use the equation: v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time taken.
0 = 25 - 9.8t
Solving for t:
9.8t = 25
t = 25 / 9.8
t ≈ 2.55 seconds
Now, let's find the time it takes for the stone to fall from the maximum height to the ground:
Since the stone is initially thrown up, it will take the same amount of time to reach the highest point and then come back down to the ground. So, the total time of flight (T) is twice the time it took to reach the maximum height, which is:
T = 2 × t
T = 2 × 2.55
T ≈ 5.10 seconds
Finally, let's find the speed of the stone as it strikes the ground. Using the equation v = u + at, where u is the initial velocity and a is the acceleration due to gravity:
v = 25 - 9.8T
Substituting the value of T, we get:
v = 25 - 9.8 × 5.10
v ≈ -49.8 m/s
Note: The negative sign indicates that the velocity is in the opposite direction of the initial velocity, which means the stone is moving downward.
Therefore, the speed of the stone as it strikes the ground is approximately 49.8 m/s.