Legolas shoots a flaming arrow straight up into the air (from a distance of 2.6 meters from the ground) at 42 meters per second. The gravitational pull of the Earth is about 4.9 meters per second squared.
Which quadratic equation correctly models this situation, where h represents the height of the arrow after t seconds?
h=42t2+4.96t−2.6
h=2.6t2−42t−9.86
h=−4.9t2+42t+2.6
h=−9.86(t−42)(t+2.6)
if you meant to type h=−4.9t^2+42t+2.6 , that would be it
To determine the correct quadratic equation that models the given situation, we need to analyze the information provided.
The equation of motion for an object in free fall near the surface of the Earth is given by:
h = -gt^2 + vt + h0
where:
h is the height (in meters) at time t (in seconds)
g is the acceleration due to gravity (approximately 9.8 m/s^2)
v is the initial velocity (in this case, upward velocity)
h0 is the initial height or position (in this case, 2.6 meters)
Given that the initial velocity is 42 m/s and the gravitational pull is approximately 4.9 m/s^2, we can rewrite the equation as:
h = -4.9t^2 + 42t + 2.6
Therefore, the correct quadratic equation that models this situation is:
h = -4.9t^2 + 42t + 2.6
Thus, the option h=−4.9t^2+42t+2.6 correctly represents the given situation.