When we estimate distances from velocity data, it is sometimes necessary to use times t0, t1, t2, t3, . . that are not equally spaced. we can still estimate distances using the time periods δti = ti − ti − 1. for example, a space shuttle was launched on a mission, the purpose of which was to install a new motor in a satellite. the table provided gives the velocity data for the shuttle between liftoff and the jettisoning of the solid rocket boosters. use these data to estimate the height, h, above earth's surface of the space shuttle, 62 seconds after liftoff. (give the upper approximation available from the data.) h = ft event time (s) velocity (ft/s) launch 0 0 begin roll maneuver 10 180 end roll maneuver 15 319 throttle to 89% 20 453 throttle to 67% 32 742 throttle to 104% 59 1100 maximum dynamic pressure 62 1430 solid rocket booster separation 125 4151

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Answer: a charge of -1.0  × 10⁻⁴ c must be placed  at x = 26 m.the sign of the charge will be the same sign as the  -4.0  µc charge.======electricstatic force between two point charges  is given by    where k is coulomb's constant,  8.99×10⁹  n·m²/c², q₁ and q₂ are the point charges, and r is the distance between the two point charges.assign positive to q₁let q₁ =  6.0 µc, q₂ = -4.0  µc, q₀ represent the charge at the origin, and q₃ represent this new charge to place.the charge at the origin q₀ would experience the following force f₀₁ from q₁, with r = 6.0 m (note that 1  µc = 10⁻⁶ c)    the force from q₂    the force from q₃    the net force on the origin charge, q₀, has to be zero for no electrostatic forcehaving an equation where k and q₀ can be divided out of the equation will allow us to solve for q₃    isolating:     a charge of -1.0  × 10⁻⁴ c must be placed  at x = 26 m.the sign of the charge will be the same as the  -4.0  µc charge