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A football player kicks a ball with an initial velocity of 30 meters per second at an angle of 53° above the horizontal. how long will the ball be in the air for

Respuesta :

LammettHash

At time t, the ball attains a height y of

y = (30 m/s) sin(53Âș) t - 1/2 g tÂČ

where g = 9.80 m/sÂČ is the magnitude of the acceleration due to gravity.

Solve for t when y = 0:

(30 m/s) sin(53Âș) t - 1/2 g tÂČ = 0

t ((30 m/s) sin(53Âș) - (4.90 m/sÂČ) t ) = 0

t = 0   or   (30 m/s) sin(53Âș) - (4.90 m/sÂČ) t = 0

We ignore the first solution, since that refers to the moment the ball is kicked.

(30 m/s) sin(53Âș) - (4.90 m/sÂČ) t = 0

(30 m/s) sin(53Âș) = (4.90 m/sÂČ) t

t = (30 m/s) sin(53Âș) / (4.90 m/sÂČ)

t ≈ 4.9 s

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