Question

Rising balloon. A hot air balloon rises straight up at a rate of 120 ft per min. The balloon is tracked from a rangefinder on the ground at point p, which is 400 ft from the release point q of the balloon. Let d = the distance from the balloon to the rangefinder and t= the time in mins, since the balloon was released. Express d as a function of t.

Answer 1

Given

balloon rises straight up at a rate of 120 ft per min.

balloon is tracked from a rangefinder on the ground at point p, which is 400 ft from the release point q of the balloon.

d = the distance from the balloon to the rangefinder and t= the time in mins

Express d as a function of t.

To proof = With the help the diagram as shown in below .

balloon rises straight up at a rate of 120 ft per min.

thus RQ = 120t

rangefinder on the ground at point p, which is 400 ft from the release point q of the balloon.

thus PQ = 400 ft

Let PR =d

by using the pythagoras theorem

we have

RQ² + PQ² = PR²

now putting the value

we have

(120t)² + 400² = d²

`\sqrt{120t^(2) + 400^(2)}` = d

`\sqrt{14400t^(2) + 160000 }` = d

`\sqrt{1600(9t^(2) + 100) }` = d

`d=40\sqrt{9t^(2) + 100}` ft

hence d is express in the term of t

Hence proved