A rocket is launched from the top of a 70 foot cliff with an ititial velocity of 100 feet per second. The height, h, of the rocket after t seconds is givin by the equation h=-16t^2 +100t + 70/ How laong after the rocket is launched will it be 30 feet from the ground. round to the nearest tenth
+23246 Given the formula: h = -16t2 + 100t + 70 and given the value: h = 30, what is the value of t?
30 = -16t2 + 100t + 70
0 = -16t2 + 100t + 40 subtract 30 from both sides
0 = -4t2 + 25t + 10 divide both sides by 4
a = -4 b = 25 c = 10 use the quadratic formula
t = [ -b +/- sqrt( b2 - 4·a·c ) ] / (2·a)
t = [ -25 +/- sqrt( (25)2 - 4·(-4)·(10 ) ] / (2·-4)
t = [ -25 +/- sqrt( 625 + 160) ] / (-8)
t = [ -25 +/- sqrt( 785) ] / (-8)
t = -0,377 or t = 6.627
Since t must be positive, t = 6.6
+23246 Given the formula: h = -16t2 + 100t + 70 and given the value: h = 30, what is the value of t?
30 = -16t2 + 100t + 70
0 = -16t2 + 100t + 40 subtract 30 from both sides
0 = -4t2 + 25t + 10 divide both sides by 4
a = -4 b = 25 c = 10 use the quadratic formula
t = [ -b +/- sqrt( b2 - 4·a·c ) ] / (2·a)
t = [ -25 +/- sqrt( (25)2 - 4·(-4)·(10 ) ] / (2·-4)
t = [ -25 +/- sqrt( 625 + 160) ] / (-8)
t = [ -25 +/- sqrt( 785) ] / (-8)
t = -0,377 or t = 6.627
Since t must be positive, t = 6.6
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