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 need to use the equations of motion.
First, let's consider the upward motion of the stone. We can use the equation:
v = u + gt
where:
v is the final velocity (unknown)
u is the initial velocity (25 m/s, upward)
g is the acceleration due to gravity (-9.8 m/s^2, downward)
t is the time it takes for the stone to reach its highest point and then fall back down (unknown)
At the highest point, the vertical velocity becomes zero because the stone momentarily stops before it starts to fall back down. So, we can use this information to find the time until it reaches the highest point:
v = u + gt
0 = 25 - 9.8t
9.8t = 25
t = 25 / 9.8
t ≈ 2.55 seconds
Now we have the time it takes for the stone to reach its highest point. To find the total time of flight, we need to double the time taken to reach the highest point:
Total time of flight = 2t ≈ 2 × 2.55 ≈ 5.1 seconds
Using this total time of flight, we can find the final velocity of the stone as it strikes the ground. We'll use the equation:
v = u + gt
where:
v is the final velocity (unknown)
u is the initial velocity (25 m/s, upward)
g is the acceleration due to gravity (-9.8 m/s^2, downward)
t is the total time of flight (5.1 seconds)
v = 25 - 9.8 × 5.1
v = 25 - 49.8
v ≈ -24.8 m/s
Since the velocity is negative, it indicates that the stone is moving downward. To find the speed at which the stone strikes the ground, we take the absolute value:
Speed = |v| ≈ |-24.8| ≈ 24.8 m/s
Therefore, the speed of the stone as it strikes the ground is approximately 24.8 m/s.