A potato was launched in the air using a potato gun. The function for the situation was h(t) = -16t2 + 100t + 10, where t was the time in seconds and h(t) was the height in feet. (3 points each)

a. What was the maximum height of the potato?

b. What was the lowest height of the potato?

c. What was the lowest time that applies to the actual situation?

d. What is the greatest time that applied to the actual situation?

e. Using your answers to parts a through d, what are the domain and range of the function, as they apply to this situation? Use set builder notation.

Aspacecraft can attain a stable orbit 300 kilometers above earth if it reaches a velocity of 7.7 kilometers per second. the formula for a rocket's maximum velocity v in kilometers per second is vequalsminus0.0098tplusc ln upper r, where t is the firing time in seconds, c is the velocity of the exhaust in kilometers per second, and r is the ratio of the mass of the rocket filled with fuel to the mass of the rocket without fuel. find the velocity of a spacecraft whose booster rocket has a mass ratio of 20, an exhaust velocity of 2.1 km/s, and a firing time of 15 s. can the spacecraft achieve a stable orbit 300 km above earth?