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ball is thrown straight down from the top of a 425-foot building with an initial velocity of -22 feet per second. Use the position function below for free-falling objects. s(t)-16t+ vot + so What is its velocity after 2 seconds? v(2) -81 ft/s What is its velocity after falling 344 feet? VW ft/s Viewing Seved Work Revert to Last Res Submit Answer

User Grigoryvp
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Final answer:

The velocity of the ball after 2 seconds is -86 ft/s. The velocity of the ball after falling 344 feet is -170.48 ft/s.

Step-by-step explanation:

To find the velocity of the ball after 2 seconds, we need to substitute the value of t = 2 into the velocity function. The velocity function is given as v(t) = -32t + vo, where vo is the initial velocity. Given that the initial velocity is -22 ft/s, we can calculate the velocity after 2 seconds using v(2) = -32(2) + (-22) = -64 -22 = -86 ft/s.

To find the velocity after falling 344 feet, we need to find the time it takes to fall 344 feet and then substitute this time into the velocity function. The equation for the distance fallen is given as s(t) = -16t^2 + vot + so, where so is the initial position. Given that the initial position is 425 feet, we can set s(t) = 425 - 344 = 81 and solve for t. The equation becomes 81 = -16t^2 - 22t + 425. By solving this quadratic equation, we find two possible values for t: t = -5.64 s and t = 4.64 s. Since time cannot be negative in this case, we can disregard the negative value. Thus, the velocity after falling 344 feet is v(4.64) = -32(4.64) + (-22) = -148.48 - 22 = -170.48 ft/s.

User Nissan
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Final answer:

The velocity of the ball after 2 seconds is -86 ft/s.

Step-by-step explanation:

To calculate the velocity of the ball after 2 seconds, we can substitute the given values into the velocity function:
v(t) = v0 + gt

Where:
v(t) is the velocity at time t
v0 is the initial velocity
g is the acceleration due to gravity (approximately -32 feet per second squared)

Plugging in the values:
v(2) = -22 + (-32)*2
v(2) = -22 - 64
v(2) = -86 feet per second

User Sasha Koss
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