a stone starts to fall from rest positon from of top of the hill.it hits the ground with velocity 112 m/s. how to calculate the it taks to hits the ground and hight of the hil.
To calculate the time it takes for the stone to hit the ground and the height of the hill, you can use the equations of motion. Let's break down the problem step by step.
Step 1: Find the time it takes for the stone to hit the ground.
We can use the equation of motion:
v = u + at
where:
- v is the final velocity (112 m/s),
- u is the initial velocity (since the stone starts from rest, u = 0 m/s),
- a is the acceleration (in this case, the acceleration due to gravity, which is approximately -9.8 m/s^2),
- t is the time.
Solving for time, we get:
112 m/s = 0 m/s + (-9.8 m/s^2) * t
By rearranging the equation, we find:
t = 112 m/s / 9.8 m/s^2
t ≈ 11.43 seconds
So, it takes approximately 11.43 seconds for the stone to hit the ground.
Step 2: Calculate the height of the hill.
We can use another equation of motion:
s = ut + 0.5at^2
where:
- s is the displacement (height of the hill),
- u is the initial velocity (0 m/s),
- a is the acceleration (-9.8 m/s^2),
- t is the time (11.43 seconds).
Substituting the values into the equation, we get:
s = 0 m/s * 11.43 s + 0.5 * (-9.8 m/s^2) * (11.43 s)^2
Simplifying the equation, we find:
s = 0 + 0.5 * (-9.8 m/s^2) * (130.9249 s^2)
s ≈ -642.67 m
The negative sign indicates that the height is measured below the reference point (ground level). So the magnitude of the height is approximately 642.67 meters.
Therefore, the time it takes for the stone to hit the ground is approximately 11.43 seconds, and the height of the hill is approximately 642.67 meters (below the reference point).