a small kite starts at 7 meters off the ground and rises at 2.5 meters per second. a large kite starts at 12 meters off the ground and rises at 1.5 meters per second. when are the kites at the same height?
A small kite starts at 7.3 meters off the ground and rises at 2.5 meters per second. A large kite starts at 12.4 meters off the ground and rises at 1.5 meters per second. How many seconds will the kites be the same height?
After 5 seconds
To find out when the small and large kites are at the same height, we need to set up an equation where the heights of the two kites are equal.
Let's assume 't' represents the time in seconds.
For the small kite:
Height of the small kite = 7 + 2.5t
For the large kite:
Height of the large kite = 12 + 1.5t
To find the time when the kites are at the same height, we can set up the equation:
7 + 2.5t = 12 + 1.5t
Now, let's solve this equation step-by-step:
7 + 2.5t = 12 + 1.5t
Subtract 1.5t from both sides:
7 + 2.5t - 1.5t = 12 + 1.5t - 1.5t
Simplify:
7 + t = 12
Subtract 7 from both sides:
7 + t - 7 = 12 - 7
Simplify:
t = 5
Therefore, the two kites will be at the same height after 5 seconds.
To find out when the small kite and the large kite are at the same height, we need to set up an equation based on their respective positions as functions of time.
Let's assume that t represents the time in seconds, h₁(t) represents the height of the small kite at time t, and h₂(t) represents the height of the large kite at time t.
Given that the small kite starts at 7 meters off the ground and rises at a rate of 2.5 meters per second, we can express its height as:
h₁(t) = 7 + 2.5t
Similarly, the large kite starts at 12 meters off the ground and rises at a rate of 1.5 meters per second:
h₂(t) = 12 + 1.5t
To find when both kites are at the same height, we can set their height functions equal to each other and solve for t:
7 + 2.5t = 12 + 1.5t
First, let's move all terms containing t to one side of the equation:
2.5t - 1.5t = 12 - 7
Combining like terms, we have:
1t = 5
Simplifying further, we get:
t = 5
Therefore, the kites will be at the same height after 5 seconds.