To calculate the velocity of the traditional bouncing ball just before it hits the ground for its first bounce, we can use the equations of motion.
For the traditional bouncing ball (Graph 1):
Initial height, h_i = 12 m
Final height, h_f = 0 m
Acceleration due to gravity, g = 9.81 m/s^2
Using the equation for velocity with constant acceleration:
v_f^2 = v_i^2 + 2gh
Where:
v_f = final velocity
v_i = initial velocity (0 m/s as the ball is initially dropped)
h = change in height (12 m)
Solving for v_f:
v_f^2 = 0 + 2 * 9.81 * 12
v_f = sqrt(235.44)
v_f ≈ 15.36 m/s
Therefore, the velocity of the traditional bouncing ball just before it hits the ground for its first bounce is approximately 15.36 m/s.
Now, let's calculate the velocity of the Super Bouncy ball just before it hits the ground for its first bounce (Graph 2):
Since the Super Bouncy ball keeps bouncing forever, it does not lose any kinetic energy during its bounces. Therefore, the velocity before each bounce will be the same.
From the graph, we can see that the velocity of the Super Bouncy ball just before it hits the ground for its first bounce is around 5 m/s.
Therefore, the velocity of the Super Bouncy ball just before it hits the ground for its first bounce is approximately 5 m/s.
A friend of yours would like you to invest in her new toy company. She is excited to tell you about her new product, a “Super Bouncy” ball, a ball which she claims will keep bouncing forever. She shows you two sets of data represented in graphs 1 and 2 below. Both balls have the same mass of 0.25 kg. Both balls are held at a height of 12 m at t = 0 seconds. = 0 s. Show your work and use correct units for full credit. b. Apply mathematical concepts and processes to calculate the velocity of the traditional bouncing ball and the Super Bouncy ball just before it hits the ground for its first bounce
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