A basketball game began with a jump-ball at center court. When the ball left the referee's hand it was 1.6 m above the gym floor and moving upward at 5.5 m/s.
a) How long did the ball take to stop moving?
b) How high above the floor was the ball when it stopped rising?
h = -4.9t^2 + 5.5t + 1.6
simply find the vertex of this parabola using your most favourite method and you
have both answers.
To find the answers to these questions, we need to analyze the motion of the ball. This can be done using the equations of motion.
a) How long did the ball take to stop moving?
To determine the time it takes for the ball to stop moving, we need to find the time it takes for the ball's velocity to reach 0 m/s. We can use the equation of motion:
v = u + at
where:
- v is the final velocity (0 m/s in this case, as the ball stops)
- u is the initial velocity (5.5 m/s, as the ball was moving upward)
- a is the acceleration (which is due to gravity and is approximately -9.8 m/s^2, taking downward as negative)
Rearranging the equation, we get:
t = (v - u) / a
Substituting the values into the equation, we have:
t = (0 - 5.5) / (-9.8) = 0.561 seconds
Therefore, the ball took approximately 0.561 seconds to stop moving.
b) How high above the floor was the ball when it stopped rising?
To find the height above the floor when the ball stopped rising, we can use the equation of motion:
s = ut + (1/2)at^2
where:
- s is the displacement (height in this case)
- u is the initial velocity (5.5 m/s, as the ball was moving upward)
- t is the time (0.561 seconds, as we found in part a)
- a is the acceleration (which is due to gravity and is approximately -9.8 m/s^2, taking downward as negative)
Substituting the values into the equation, we have:
s = (5.5 x 0.561) + (0.5 x -9.8 x (0.561)^2)
= 3.082 + (-1.63)
= 1.452 meters
Therefore, the ball was approximately 1.452 meters above the floor when it stopped rising.