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