# 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

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

### 1 thought on “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”

1. ThanhThu
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.