Question

A small kite starts at 7.3 meters off the ground and girs up at 2.5 meters per second. A large kite starts at 12 .4 meters off the ground and goes up at 1.5 meters per second. When are the kites at the same height

Answer 1

Let "t" be the time in seconds at which both the kites are at the same height.

Now, for the small kite which starts at 7.3 meters off the ground, and has a speed of 2.5 meters per second, let the height at which it will be at the same height as the second kite be "h". Then, h can be written in terms of t as:

$h=7.3+2.5t$....Equation 1

Likewise, for the large kite which starts at 12.4 meters off the ground and goes up at 1.5 meters per second, the height at which it will be at the same height as the small kite will again be:

$h=12.4+1.5t$...Equation 2

Since the height is the same, Equation 1=Equation 2

$7.3+2.5t=12.4+1.5t$

Thus, $t=5.1$ seconds.

Now, at t=5.1 seconds, the height can be found by substituting t=5.1 to any one of the two equations (Equation 1 or Equation 2).

Thus, Equation 1 will give us:

$7.3+2.5\times 5.1=20.05$ meters.

Therefore, the kites are at the same height when the time is 5.1 seconds from start and the value of that same height is 20.05 meters.