Help please?

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1 Answer
Apr 23, 2018

#"The projectile reaches the ground after 6 seconds."#

Explanation:

#v_0 = 20 m/s#
#h_0 = 60 m#
#h = h_0 + v_{0y} t - g t^2/2#

#"Take g = 10 m/s² for simplicity (gravity constant)"#
#"(normally it is 9.81 m/s²)"#
#=> 75 = 60 + v_{0y} * 1 - 10.0 * 1^2 / 2#
#=> 15 = v_{0y} - 5.0#
#=> 20.0 = v_{0y}#
#=> 80 = 60 + v_{0y} * 2 - 10.0 * 2^2 / 2#
#=> 20 = 2 * v_{0y} - 20.0#
#=> v_{0y} = 20 m/s#

#v_{0y} = v_0 => " The projectile is fired vertically upwards."#

#"So the data in the table are consistent with the physical"#
#"laws of falling under gravity."#

#"So the formula is : "#

#d = 60 + 20*t - 5*t^2#

#"Now the projectile reaches the ground when d=0 :"#

#0 = 60 + 20*t - 5*t^2#

#"This is a quadratic equation that can be simplified by dividing"#
#"both sides through -5 :"#

# t^2 - 4 t - 12 = 0#

#"The discriminant is : "4^2 + 12*4 = 64 = 8^2#

#=> t = (4 pm 8)/2 = cancel(-2) or 6#

#"(t = -2 is not possible physically so t = 6 remains)"#

#=> t = 6" seconds"#

#"Note that the graph is a parabole."#