A projectile was launched from the ground with a certain initial velocity. Militaries used a radar to determine the vertical coordinate y(t) of the projectile for two moments of time t measured in seconds from the moment when the projectile was launched. The radar measurements showed that y(2) = 269 meters, y(5) = 565 meters. Calculate the maximum of y(t) if it is known as follows: 1. The projectile was moving along a vertical line. 2. The acceleration due to gravity g is 9.81 meter/seconda. 3. There is a resistance proportional to the velocity of the projectile. 4. The value of the empirical coefficient p is a constant. 5. Distances are measured in meters. A student solved the problem, rounded-off the numerical value of the maximum of y(t) to THREE significant figures and presented it below (15 points): meters (your numerical answer must be written here) Also, it is required to answer several additional questions as follows: 1. If p is the value of a positive empirical constant (its value is to be found), v, is the unknown initial velocity of the projectile, then the formula for the altitude y of the projectile at the moment of time t is given by the formula (1 point): ept 1-e-pt 9.81 y = - р 9.81 y = t + (V0 - P 9.81 y=- t + (vo + 381 981 t + (vo + 9.82) P 1-e-pt P 5 1-e-pt t-(v. + 9.81 P P 9.81 y = P 9.81 y = 2 9.81 t? + VO t- t P 2. If p is the value of a positive empirical constant (its value is to be found), vo is the unknown initial velocity of the projectile, then the value of the velocity v of the projectile at the moment of time t is given by the formula (1 point): ept ept 9.81 9.81 V=- + (Vo + p P 9.81 9.81 V= + (VO- p р 9.81 V = р 9.81 ept +(v. + 9.81) (vo + 981) 1-e-pt р P v = vo - 9.81 t-pt 3. The maximum of the altitude is achieved when time t (measured in seconds and rounded-off to FOUR significant figures) is equal to (3 points): 9.354 10.49 11.96 12.39 12.47