Final answer:
To calculate the speed at impact, we use the ratio of the squares of the speeds and kinematic equations. Exact speed cannot be determined without additional information such as coefficient of friction and distance to the truck. Accident reconstruction experts perform such calculations.
Step-by-step explanation:
Calculating the Speed at Impact
To determine the speed at which you would be traveling when you hit the truck, we need to consider the physics involved in the situation. Assuming both cars are identical and that the braking forces are the same, Granny stops just before the truck thanks to an earlier deceleration from a lower speed. You, however, were initially traveling at 70 mph. The stopping distance for each vehicle is proportional to the square of the velocity. Thus, we can set up a ratio of the squares of the speeds to find the distance you would travel before coming to a stop.
Given that Granny was traveling at 50 mph and stopped just in time, we can use the ratio (70 mph / 50 mph) squared to estimate the stopping distance you would need. Given that your stopping distance will be longer due to the higher speed, when Granny stops, you will still be moving. The exact speed can be calculated using the kinematic equation: v^2 = u^2 + 2as, where 'v' is the final velocity (which would be zero for a complete stop), 'u' is the initial velocity, 'a' is the acceleration (deceleration in this case), and 's' is the stopping distance. For a precise answer, we would also need to know the coefficient of friction and the distance to the overturned truck.
Without the exact values for these variables, an approximate answer cannot be accurately determined. In situations like these, calculations are typically carried out by accident reconstruction experts who take into account numerous variables to determine the velocity at impact.