Here the missing Infos ;-)).
The Physics of Baseball by Robert Adair -
after t seconds, starting 1 sec after 35 angle, rotating with an initial backspin of 2000 revolutions per minute, and hit about 110mph is given by
H(t)= -80t^2+340t-260 (in feet)
a)how many seconds willpass before the ball hits the ground?
The distance travelded by the ball is given by
D(t)= -5t^2+115t-110 (in feet)
b)How far will the ball travel before it hits the ground?
c)Using D(t), how far will a ball travel in 6 seconds, the time it takes it takes a high fly ball to hin the ground?
a) just plug in H=0 and solve for t
t = 1, 13/4
b) just plug in t = 13/4
D(3.25) = 210.9
c) D(6) = 400 ft
To answer these questions, we need to use the provided equations. Let's go step by step:
a) To determine the time it takes for the ball to hit the ground, we need to find the value of t when H(t) = 0. Since H(t) is the height of the ball, when it hits the ground, the height is 0.
Therefore, we need to solve the equation -80t^2 + 340t - 260 = 0 for t.
To solve this quadratic equation, we can use the quadratic formula:
t = (-b ± √(b^2 - 4ac)) / (2a)
For our equation, a = -80, b = 340, and c = -260.
Plugging these values into the quadratic formula, we get:
t = (-340 ± √((340)^2 - 4(-80)(-260))) / (2(-80))
After simplifying and calculating, we find two possible values for t: t ≈ 0.95 seconds and t ≈ 3.45 seconds.
However, we were told to find the time after 1 second, so we discard the value t ≈ 0.95 seconds. Therefore, the ball will hit the ground approximately 3.45 seconds after 1 second.
b) To find how far the ball will travel before it hits the ground, we need to evaluate D(t) when t = 3.45 seconds (the time it takes for the ball to hit the ground).
D(t) = -5t^2 + 115t - 110
Plugging in t = 3.45, we get:
D(3.45) = -5(3.45)^2 + 115(3.45) - 110
After calculating, we find that D(3.45) is approximately 288.525 feet.
Therefore, the ball will travel approximately 288.525 feet before it hits the ground.
c) To find how far the ball will travel in 6 seconds, we can again use the equation D(t):
D(t) = -5t^2 + 115t - 110
Plugging in t = 6, we get:
D(6) = -5(6)^2 + 115(6) - 110
After calculating, we find that D(6) is approximately 70 feet.
Therefore, the ball will travel approximately 70 feet in 6 seconds.
I hope this helps! Let me know if you have any further questions.