a boy throws a stone straight upward with an initial speed of 15 m/s on the surface of the earth. what maximum height above the starting point will the stone reach before falling back down?
h = (V^2-Vo^2)/2g
h = (0-225) / -19.6 = 11.48 m.
To find the maximum height above the starting point that the stone will reach before falling back down, we can use the following steps:
Step 1: Determine the initial velocity of the stone, which is given as 15 m/s.
Step 2: Calculate the time it takes for the stone to reach its highest point. To do this, we need to consider the fact that the stone is launched vertically and will experience free-fall motion. The formula to calculate the time of flight is:
time = (2 * initial velocity) / (acceleration due to gravity)
The acceleration due to gravity on the surface of the Earth is approximately 9.8 m/s².
Using this formula, we can calculate the time it takes for the stone to reach its highest point:
time = (2 * 15 m/s) / (9.8 m/s²)
time ≈ 3.06 seconds
Step 3: Calculate the maximum height reached by the stone using the formula:
height = (initial velocity * time) - (0.5 * acceleration due to gravity * time²)
height = (15 m/s * 3.06 s) - (0.5 * 9.8 m/s² * (3.06 s)²)
height ≈ 46.23 meters
Therefore, the stone will reach a maximum height of approximately 46.23 meters above the starting point before falling back down.
To find the maximum height reached by the stone, we can use the equations of motion.
Step 1: Identify the given information.
- Initial velocity (u) = 15 m/s (upward)
- Acceleration due to gravity (a) = -9.8 m/s² (downward, as it opposes the stone's upward motion)
Step 2: Determine the time taken to reach the maximum height.
At the highest point, the stone's final velocity (v) will become zero before it falls back down. We can use the equation v = u + at to find the time taken (t) to reach this point.
v = 0 m/s (at the highest point)
u = 15 m/s (upward)
a = -9.8 m/s² (downward)
0 = 15 - 9.8t
9.8t = 15
t = 15 / 9.8 ≈ 1.53 seconds
Step 3: Calculate the maximum height.
To find the maximum height (H), we can use the equation H = ut + (1/2)at².
H = 15 * 1.53 + (1/2) * (-9.8) * (1.53)²
H ≈ 22.84 meters
Therefore, the maximum height reached by the stone before falling back down is approximately 22.84 meters.