Pre calculus word <span title="problem.........................?">problem.....................</span>

Question

An airplane flying over head at a rate of 350 mph(513.33 ft/sec) at an altitude of 10,000 ft is first spotted by an observer who estimates his angle of elevation to the plane to be 22 degree. Determine a function that relates the horizontal distance between the observer and the plane and the seconds after the observer first spots the plane. When will the plane be directly overhead?

Answer 1

function:

f(x)= (10000/tan(22))- 513.33*t

where t= time in seconds.

overhead:

2200.791116 seconds

Answer 2

v = x/t

x = vt

initial distance xi = 10000 cos 22 deg = 9271 ft

x(t) = 9271 - vt

x(t) = 9271 - 513.33 t

if plane is overhead, x(t) = 0,

0 = 9271 - 513.33 t

t = 9271/513.33

t = 28 sec