If a ball is thrown straight up into the air with an initial velocity of 45 ft/s, it's height in feet after t second is given by y = 45t - 16t^2
a] find the average velocity for the time period begining when t = 2 and lasting.
i) 0.1 seconds
ii) 0.001 seconds
iii) 0.0001 seconds

b) Estimate the instantaneous velocity of the ball when t = 2

Question

23-08-2022
Mathematics

Answered

If a ball is thrown straight up into the air with an initial velocity of 45 ft/s, it's height in feet after t second is given by y = 45t - 16t^2
a] find the average velocity for the time period begining when t = 2 and lasting.
i) 0.1 seconds
ii) 0.001 seconds
iii) 0.0001 seconds

b) Estimate the instantaneous velocity of the ball when t = 2

Answer :

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abiolataiwo2015 abiolataiwo2015 · Answer 1 · 2022-08-25T12:19:24-04:00

The average velocity for the time period beginning when t = 2 and lasting is: -19.016 ft/sec. The instantaneous velocity of the ball when t = 2 is: 19 ft/sec.

Average velocity

Velocity = 45-32t

When t=2

v(2) = 45-32(2)

v(2) =45-64

v(2) = -19 ft per second ( downward direction)

Velocity=45-32t

When t=2.1

v(2.1) = 45-32(2.1)

v(2.1) = 45-67.2

v(2.1) = -22.2 ft per second

Average velocity from t=2 to t=2.1

Average velocity= (-19-22.2)/2

Average velocity= -41.2/2

Average velocity=-20.5 ft/sec

Velocity=45-32t

When t=2.001

v(2.001) = 45-32(2.001)

v(2.001) = 45-64.032

v(2.001) = -19.032.

Average velocity from t=2 to 2.001

Average velocity = (-19-19.032)/2

Average velocity = -19.016 ft/sec

Velocity=45-32t

When t=2.0001

v(2.0001) = 45-32(2.0001)

v(2.0001) =45-64.0032

v(2.0001) = -19.0032

Average velocity from t=2 to 2.0001

Average velocity= (-19-19.0032)/2

Average velocity = -19.0016 ft/sec

b. Instantaneous v at t=2

Instantaneous = -19 ft/sec

Therefore The average velocity for the time period beginning when t = 2 and lasting is: -19.016 ft/sec. The instantaneous velocity of the ball when t = 2 is: 19 ft/sec.

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