find the height in feet of a ball after 6 seconds in the air. after one second the ball is 148 feet in the air; after 2 seconds it is 272 feet in the air
You divide by 6 afterwards ??
To find the height of the ball after 6 seconds, we can use the information given. We can start by finding the rate at which the height is changing.
After 1 second: Height = 148 ft
After 2 seconds: Height = 272 ft
To find the rate at which the height is changing, we can subtract the initial height from the final height and divide it by the time interval:
Rate of Change = (Final Height - Initial Height) / Time Interval
Rate of Change = (272 ft - 148 ft) / (2 seconds - 1 second)
Rate of Change = 124 ft/second
The rate of change tells us that the height of the ball is increasing by 124 feet for every second it is in the air.
To find the height after 6 seconds, we can multiply the rate of change by the time:
Height after 6 seconds = Initial Height + (Rate of Change × Time)
Height after 6 seconds = 148 ft + (124 ft/second × 6 seconds)
Height after 6 seconds = 148 ft + 744 ft
Height after 6 seconds = 892 ft
Therefore, the height of the ball after 6 seconds in the air is 892 feet.
The height y(t) is given by
y(t) = h + vt - 16t^2
h + v - 16 = 148
h + 2v - 64 = 272
So,
h=-8
v=172
y(t) = -8 + 172t - 16t^2
y(6) = 448