Tyler is on the 15th floor of a building. She throws a ball straight down from the window, which is 220 feet above the ground. How fast must she throw the ball(in feet per second) for it to hit the ground in 3 seconds?
d = Vo*t + 0.5gt^2 = 220Ft.
3Vo + 0.5 * 32 * 3^2 = 220,
3Vo + 144 = 220,
3Vo = 220 - 144 = 76,
Vo = 25.33 Ft/s.
Lily,check your 4-5-11,6:42pm post for
solution to your proportions prob.
To determine how fast Tyler must throw the ball for it to hit the ground in 3 seconds, we can use the equation of motion:
d = ut + (1/2)at^2
Where:
d = distance traveled (in this case, the height of the building)
u = initial velocity (what we're trying to find)
t = time taken (in this case, 3 seconds)
a = acceleration due to gravity (approximately -32.2 ft/s^2)
Since Tyler throws the ball straight down, the initial velocity will be negative (opposite to the direction of gravity). The height of the building is 220 feet, and the time taken is 3 seconds. The acceleration due to gravity remains constant at approximately -32.2 ft/s^2.
Plugging in the values into the equation, we have:
220 = u * 3 + (1/2) * (-32.2) * (3^2)
Simplifying the equation, we get:
220 = 3u - 16.1 * 9
220 = 3u - 144.9
Add 144.9 to both sides:
220 + 144.9 = 3u
364.9 = 3u
Divide both sides by 3:
u = 364.9 / 3
u ≈ 121.63
Therefore, Tyler must throw the ball at a speed of approximately 121.63 feet per second for it to hit the ground in 3 seconds.