MATH 1211 Written Assignment 6 - University of the People

UNIT 6 WRITTEN ASSIGNMENT

MATH 1211: CALCULUS

UNIVERSITY OF THE PEOPLE

, 1. An airplane is flying towards a radar station at a constant height of 6 km
above the ground. If the distance s between the airplane and the radar station
is decreasing at a rate of 400 km per hour when s=10 km., what is the
horizontal speed of the plane? Make sure your answer includes units.
Solution
Let assume that the horizontal distance of the plane from the radar station is
denoted by a. therefore, a right-angled triangle is formed with sides b and a, and
hypotenuses s. note that b is the constant height of 6km. using Pythagorean
theorem, we can write the formular for the problem
S2=a2+b2………(1)
Differentiate both sides of the equation in respect to time(t) by keeping b as a
constant.
a
(¿ ¿ 2+b 2)
d 2 d
s= ¿
dt dt
a
d 2
(¿¿ 2)+ (b )
dt
d 2 d
s= ¿
dt dt
ds da
2s =2a
dt dt
2 2
From equation (1), a= s -√b¿ ). Substitute the value of a into the obtained value of
da
dt

From the given information in the question, substitute 10km for s, 6 km for b, - 400
ds
km/h for dt
(since it is given that, the distance from the radar station is
decreasing at a rate of 400km per hour when s=10km) into the obtained expression
da
to get the required value of dt

da 10 km
dt
=
(√ ( 10 km )2−( 6 km )2 ) (−400 km/h)