A dog throws a bone into the air at 17.2 m/s...How high will it rise and How long will it take to reach the peak of its trajectory?
To determine the height the bone will rise and the time it takes to reach the peak of its trajectory, we can use kinematic equations.
First, we should identify the variables given:
Initial velocity (u) = 17.2 m/s
Final velocity (v) = 0 m/s (at the peak)
Acceleration (a) = -9.8 m/s² (negative due to gravity, as it is acting against the motion of the bone)
Time (t) = ?
Now we can use the kinematic equation:
v = u + at
At the peak, the final velocity (v) is 0, so the equation becomes:
0 = 17.2 - 9.8t
Rearranging the equation to solve for time (t):
9.8t = 17.2
t = 17.2 / 9.8
t ≈ 1.755 seconds
So, it will take approximately 1.755 seconds for the bone to reach the peak of its trajectory.
To find the height, we can use another kinematic equation:
v² = u² + 2as
At the peak, the final velocity (v) is 0. Rearranging the equation to solve for displacement (s):
0 = 17.2² + 2(-9.8)s
310.24 = -19.6s
s = 310.24 / -19.6
s ≈ -15.82 meters
Since height cannot be negative in this case, we take the absolute value of the result.
Therefore, the bone will rise to a height of approximately 15.82 meters.