Final answer:
To find out how long the pigeon is in the air, we set the height equation to zero and solve for t, yielding approximately 7.75 seconds, which rounds to 8 seconds.
Step-by-step explanation:
To calculate how long the pigeon is in the air, we need to find when the height h(t) is zero. The equation given is h(t) = -5t2 + 300. We can set this equation equal to zero to find when the pigeon hits the ground:
0 = -5t2 + 300
To solve for t, we can divide both sides of the equation by -5:
0 = t2 - 60
Applying the square root to both sides gives:
t = √60
The square root of 60 is approximately 7.75 seconds. However, the question asks to round to the nearest whole number, so the pigeon is in the air for approximately 8 seconds.