Question

A hot-air balloon, headed due east at an average speed of 15 miles per hour at a constant altitude of 100 feet, passes over an intersection (see the figure). Find an expression for its distance d (measured in feet) from the intersection 1 seconds later.

Answer 1

Answer:

The distance is $sqrt{10000+484t^2}$

Step-by-step explanation:

Given that,

Altitude = 100 feet

Average speed = 15 miles/ hour

We need to calculate the speed in feet/sec

Using formula for speed

$v=15 miles/hour$

$v=15\times 1.46667\ ft/sec$

$v=22\ ft/sec$

We need to calculate the distance in t sec

Using formula of speed

$v =\dfrac{d}{t}$

Put the value into the formula

$22=\dfrac{d}{t}$

$d=22t$

According to figure,

We need to calculate the distance

Using pythagorean theorem

$AC=\sqrt{(AB)^2+(BC)^2}$

Put the value into the formula

$d=\sqrt{100^2+(22t)^2$

$d=\sqrt{10000+484t^2}$

Hence, The distance is $sqrt{10000+484t^2}$