Atennis ball machine serves a ball vertically into the air from a height of 2 feet, with an initial speed of 120 feet per second. after how many seconds does the ball attain it's maximum height?

The maximum height is reached after 3.75 seconds.

Step-by-step explanation:

Assuming the deceleration due to gravity is unaided by air resistance, gravity causes the ball to lose vertical speed at the rate of 32 ft/s every second. The initial vertical speed of 120 ft/s will decline to zero when t satisfies ...

... 120 ft/s - (32 ft/s²)t = 0

... (120 ft/s)/(32 ft/s²) = t = 3.75 s

The ball will not go any higher after its vertical speed is zero.

sin(41) = 14/c

c = 14/sin(41)

c ≈ 21.34

c ≈ 21.3

a² + 14² = 21.3²

a² + 196 = 453.69

a² = 257.69

a ≈ 16.1