Final Answer:
The acceleration of the tennis ball while it is in flight is approximately -9.81 m/s².
Step-by-step explanation:
Define the given information:
Time of flight (t) = 1.63 s
Initial and final height are the same (h1 = h2)
Identify the relevant formula:
The vertical motion of the tennis ball is governed by the following equation:
h = h_0 + v_0 * t + (1/2) * a * t^2
where:
h is the height at any time t
h_0 is the initial height
v_0 is the initial velocity
a is the acceleration
t is the time
Analyze the problem:
Since the initial and final heights are the same (h1 = h2), the displacement (Δh) is zero. Therefore:
Δh = h2 - h1 = 0
Solve for the acceleration:
Substitute the known values into the equation and solve for a:
0 = 0 + v_0 * 1.63 + (1/2) * a * 1.63^2
2.6569a + 1.63v_0 = 0
We still don't have enough information to solve for a uniquely. However, we know that the acceleration due to gravity acts downwards and is approximately -9.81 m/s². Assuming no air resistance, we can use this value for a as an approximation.
Calculate the final value:
a ≈ -9.81 m/s²
Therefore, the acceleration of the tennis ball while it is in flight is approximately -9.81 m/s². This negative sign indicates that the acceleration is directed downwards.
Note: The initial velocity (v_0) is not required to solve for the acceleration in this case. However, if v_0 was known, we could solve for it as well.