[2.21] Please help me find a) and b)

A. 28.42 m/s

B. 41.21 m.

Explanation:

A. Determination of the initial velocity of the ball:

Time (t) to reach the maximum height = 2.9 s

Final velocity (v) = 0 (at maximum height)

Acceleration due to gravity (g) = –9.8 m/s² (since the ball is going against gravity)

Initial velocity (u) =?

Thus, we can obtain the initial velocity of the ball as follow:

v = u + gt

0 = u + (–9.8 × 2.9)

0 = u – 28.42

Collect like terms

u = 0 + 28.42

u = 28.42 m/s

Therefore, the initial velocity of the ball is 28.42 m/s.

B. Determination of the maximum height reached.

Final velocity (v) = 0 (at maximum height)

Acceleration due to gravity (g) = –9.8 m/s² (since the ball is going against gravity)

Initial velocity (u) = 28.42 m/s.

Maximum height (h) =?

Thus, we can obtain the maximum height reached by the ball as follow:

v² = u² + 2gh

0² = 28.42² + (2 × –9.8 × h)

0 = 807.6964 + (–19.6h)

0 = 807.6964 – 19.6h

Collect like terms

0 – 807.6964 = – 19.6h

– 807.6964 = – 19.6h

Divide both side by – 19.6

h = –807.6964 / –19.6

h = 41.21 m

Therefore, the maximum height reached by the ball is 41.21 m

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e/c, where e is its total energy