The road runner drops a boulder from a 53 meter high building. When the block is 14 meters above the ground, the 2 meter tall Wiley Coyote looks up and sees the boulder. How much time does he have to get out of the way?
V^2 = Vo^2 + 2g*h
V^2 = 0 + 19.6*(53-14) = 764.4
V = 27.65 m/s at 14 m above gnd.
h = Vo*t + 0.5g*t^2 = 14-2 = 12
27.65t + 0.5g*t^2 = 12
4.9t^2 + 27.65t - 12 = 0
Use Quadratic Formula and get:
t = 0.405 s. To get out of the way.
To determine how much time Wiley Coyote has to get out of the way, we can use the principles of motion and calculate the time it takes for the boulder to fall from its initial height to the point where Wiley Coyote sees it.
First, let's find the time it takes for the boulder to fall from the top of the building (53 meters) to the point where Wiley Coyote sees it (14 meters). We can use the equation for free fall motion:
h = (1/2) * g * t^2
where:
h = total distance fallen
g = acceleration due to gravity (approximately 9.8 m/s^2)
t = time
Rearranging the equation to solve for time (t), we get:
t = √(2h / g)
Substituting the given values:
h = 53 m - 14 m = 39 m
g = 9.8 m/s^2
t = √(2 * 39 m / 9.8 m/s^2)
Calculating this expression, we find:
t ≈ 2.99 seconds
Therefore, Wiley Coyote has approximately 2.99 seconds to get out of the way once he sees the boulder dropping.