John and Mike were runing a race. john is a faster runner so he gives Mike a head start of 4 meters before he starts the race. Mikes initial velocity is .25 m/s and accelerates at .3 m/s^2. john leaves the gate at 1 m/s and accelerates at 4.2 m/s^2. At which point do they cross paths?
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Hi,S = Vo*t + 0.5 * a * t^2Mike: O.25t + 0.5 * 3 * t^2John: 1t + 0.5 * 4.2 * t^2We have to add 4 meters so that the distances will be equal:4 + O.25t + 0.5 * 0.3 * t^2 = 1t + 0.5 * 4.2 * t^24 + 0.25t + 0.15t^2 = 1t + 2.1t^21.95t^2 + O.75t -4 = 0 195t^2 + 75t - 400 = 037t^2 + 15t - 80 = 0 Sorry have to leave now: get the t and from here get the distance. Best regards,
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