The height of an object that is projected can be modeled using the formula h=−16t2+v0t+h0, where h is the height of the object in feet, t is the number of seconds from when the object is projected, v0 is the initial speed in feet per second, and h0 is the initial height in feet.
Ramon shoots a rubber band upward from his bedroom window to see how high it will go. The window is on the second story of his home, 15 feet above the ground. The rubber band begins its journey at 18 miles per hour.
Which equation represents the height of the rubber band during the seconds after it is shot?
Note: There are 5,280 feet in a mile. Measurements are rounded to the nearest tenths place.
To determine the equation that represents the height of the rubber band during the seconds after it is shot, we need to use the formula h = -16t^2 + v0t + h0, where h is the height of the object in feet, t is the number of seconds from when the object is projected, v0 is the initial speed in feet per second, and h0 is the initial height in feet.
In this case, we are given that the rubber band is projected from a height of 15 feet (h0) and with an initial speed of 18 miles per hour (v0). We need to convert the initial speed from miles per hour to feet per second.
There are 5,280 feet in a mile, and we need to convert 18 miles per hour to feet per second:
18 miles per hour * 5,280 feet per mile / 3600 seconds per hour = 26.4 feet per second
Therefore, the initial speed (v0) is 26.4 feet per second.
Using the given values for h0 and v0 in the formula h = -16t^2 + v0t + h0, the equation representing the height of the rubber band during the seconds after it is shot is:
h = -16t^2 + 26.4t + 15 (rounded to the nearest tenths place)