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a robot fires a yellow 7" foam ball at an angle of 35° above the horizontal and a speed of 14m/s.
how long is the ball in the air (ignore air resistance)?

For 0.3 s  the ball stays in the air.

Explanation:

Given.

length (L) = 7 inch

converting to (cm) and (m) we have = 17.78 cm = 0.1778 m

Angle (θ)  = 35°

Speed (S) = 14 m/s = 1400 cm/s

t = ?

solution

The first step in this analysis of solving the projectile motion is to resolve the velocity components into both horizontal and vertical components.

v(vertical velocity) = 14 m/s * sin(35°)

                                 = 14 × 0.573576 = 8.0299

                                  = 8.0299 m/s

v(horizontal velocity)  = 14 m/s × cos (35°)

                                     = 11.468 m/s

we need to know the duration of time (T) the ball is in the air.

the formula is given as,

t = (v(horizontal) - v(vertical)) / a

a = -9.8 m/s

t = (-11.468 + 8.0299) / -9.8

t= 0.3508 s = 0.3 s

The ball stays in the air for a duration of 0.3 s

i believe the answer is a

0.19 m/s and 0.45 m/s