basketball hoop is 2.90m above the ground. Chris is 1.96m tall, and the maximum vertical distance between the tip of his hands and the bottom of his feet is 2.81m. To dunk a basketball, the tip of his hands must be at 0.190m above the basketball hoop or more. With what vertical speed must he jump in order to dunk the ball?
Ответы
To dunk the basketball, Chris needs to jump high enough so that the tip of his hands reaches 0.190m above the basketball hoop.
The vertical distance he needs to cover can be calculated as follows:
Vertical distance = (height of basketball hoop) - (height of Chris) + (minimum required height to dunk the ball)
Vertical distance = 2.90m - 1.96m + 0.190m
Vertical distance = 1.13m
To calculate the required vertical speed for Chris to jump, we can use the kinematic equation:
vf^2 = vi^2 + 2ad
where
• vf = is the final vertical velocity (which we want to find)
• vi = is the initial vertical velocity (which is 0 since Chris is starting from rest)
• a is the acceleration due to gravity, which is -9.81 m/s^2 (negative because it is acting in the opposite direction to the jump)
• d is the vertical distance Chris needs to cover, which is 1.13m
Plugging in these values, we get:
vf^2 = 2(9.81)(1.13)
vf^2 = 22.2453
vf = sqrt(22.2453)
vf = 4.71 m/s (rounded to two decimal places)
Therefore, Chris needs to jump with a vertical speed of 4.71 m/s or higher to dunk the basketball.