A car traveling at a constant speed of 48 m/s passes a trooper hidden behind a billboard. Three seconds after the speeding car passes the billboard, the trooper sets out from the billboard to catch it, accelerating at a constant rate of 3.2 m/s². How far from the billboard will the car be when the policeman catches up?
Answers
Answer:
31.0
Explanation:
푥푐푎푟=푥푡푟표표푝푒푟,푥0푐푎푟+푣푐푎푟푡=푥0푡푟표표푝푒푟+푣푡푟표표푝푒푟푡+12푎푡2,푥0푐푎푟+푣푐푎푟푡=12푎푡2,45+45푡=12∙3푡2,
3푡2−90푡−90=0,푡2−30푡−30=0.This quadratic equation has 2 roots (sincethetime can’t be negative we choose the positive root):푡=−푏±√푏2−4푎푐2푎=−(−30)±√302−4∙1∙(−30)2∙1,푡=30+√10202=30.9푠≈31.0푠.Answer:푡=31.0푠
Answer:
Explanation:
Transcribed image text: A car traveling at a constant speed of 48.5 m/s passes a trooper on a motorcycle hidden behind a billboard. One second after the speeding car passes the billboard, the trooper sets out from the billboard to catch the car, accelerating at a constant rate of 2.00 m/s. How long does it take the trooper to overtake the car? Solve this problem by a graphical method. On the same graph plot position versus time for the car (solid black line) and the trooper (dashed blue line). x (km) x (km) 3 0.5 30 40 10 30 40 x (km) 3.0 x (km) 0.5 0.5 t (s) 20 30 40 50 t (s) 30 40 From the intersection of the two curves read the time (in s) at which the trooper overtakes the car X S