The height, in metres, of an arrow fired horizontally from the top of a castle is modelled by the function f(t), where f(0) = 35. Given that f′(t) = −9.8t,

a. Find f(t).

b. Determine the height of the arrow when t = 1.5.

c. Write down the height of the castle according to this model.

d. Estimate the time it will take the arrow to hit the ground.

e. State one assumption used in your calculation.