Question

A small kite starts at 7.3 meters off the ground and rises at 2.9 meters per second. A large kite starts at 18.5 meters off the ground and rises at 1.5 meters per second. Determine how many seconds it will take for the two kites to be at the same height.

A) 2.0 seconds
B) 4.0 seconds
C) 5.0 seconds
D) 6.0 seconds

Answer 1

The two kites will be at the same height after 8.0 seconds. This is found by setting up equations for each kite's height over time, equating them, and solving for time.

Step-by-step explanation:

To determine when the two kites will be at the same height, we can set up an equation for each kite's height as a function of time. Let t be the time in seconds after both kites have started moving.

The small kite's height as a function of time will be:

• Height(t) = 7.3 + 2.9t

And the large kite's height as a function of time will be:

• Height(t) = 18.5 + 1.5t

To find when they are at the same height, we set the two equations equal to each other and solve for t:

7.3 + 2.9t = 18.5 + 1.5t

Now, we'll combine like terms by subtracting 1.5t from both sides:

7.3 + 1.4t = 18.5

Then, subtract 7.3 from both sides:

1.4t = 11.2

Finally, divide both sides by 1.4 to solve for t:

t = 11.2 / 1.4

t = 8.0 seconds

Therefore, it will take 8.0 seconds for the two kites to be at the same height.