Final answer:
The time it takes for the bowling pin to reach its peak height is approximately 0.837 seconds.
Step-by-step explanation:
When a juggler throws a bowling pin straight up with an initial velocity of 8.2 m/s, you can use the equations of motion to calculate the time it takes for the bowling pin to reach its peak height. The equation to use in this case is:
vf = vi + gt
Where:
- vf = final velocity of the bowling pin (which is 0 m/s at its peak)
- vi = initial velocity of the bowling pin (8.2 m/s)
- g = acceleration due to gravity (-9.8 m/s^2)
- t = time taken
Substituting the given values into the equation and solving for t, you get:
0 = 8.2 + (-9.8)t
t = 8.2 / 9.8
t = 0.837 s
Therefore, it takes approximately 0.837 seconds for the bowling pin to reach its peak height.