Final answer:
To calculate how fast the ball was thrown, use the equation v = u + gt, where v is the final velocity, u is the initial velocity, g is the acceleration due to gravity, and t is the time taken. To calculate the time in the air to reach the maximum height, use the equation t = (v - u) / g.
Step-by-step explanation:
(a) To calculate how fast the ball was thrown, we need to first determine the time it takes for the ball to reach its maximum height. We can use the equation:
v = u + gt
Where:
- v is the final velocity (0 m/s at maximum height)
- u is the initial velocity (what we are trying to find)
- g is the acceleration due to gravity (-9.8 m/s^2)
- t is the time taken to reach the maximum height
Substituting the values, we have:
0 = u - 9.8t
Solving for u, we get:
u = 9.8t
(b) To calculate the time in the air to reach the maximum height, we can use the equation:
t = (v - u) / g
Where:
- t is the time taken (what we are trying to find)
- v is the final velocity (0 m/s at maximum height)
- u is the initial velocity (9.8t, as calculated in part a)
- g is the acceleration due to gravity (-9.8 m/s^2)
Substituting the values, we have:
t = (0 - 9.8t) / -9.8
Simplifying the equation, we get:
t^2 = 2t
t = 0 or t = 2
Since time cannot be negative, the ball takes 2 seconds to reach the maximum height.