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You are piloting a helicopter which is rising vertically at a uniform velocity of 14.70 m/s. When you reach 196.00 m, you see Barney. You project a banana with a horizontal velocity of 8.50 m/s from the rising helicopter, with the mean intent to get Barney. When does the banana reach Barney's head, if he is 1.70m tall?

Respuesta :

opudodennis

Answer:

7.97 seconds

Explanation:

Distance to travel is 196-1.7=194.3m

Considering that this is vertical motion then using the equation of motion

[tex]s=-ut+0.5at^{2}[/tex] where s is the distance to travel, u is initial velocity, t is timw and g is acceleration due to gravity

Substituting s for 194.3, u for 14.7 m/s and a for 9.8

[tex]194.3=-14.7t+0.5*9.8*t^{2}[/tex]

[tex]4.9t^{2}-14.7t-194.3=0[/tex]

This is a quadratic equation which is in the form of [tex]ax^{2}+bx+c[/tex] then to solve x we use quadratic formula

t=(14.7+\sqrt (14.7^{2}-(4*4.9*-194.3))/(2*4.9)

t=7.97 seconds

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