The acceleration due to gravity on the planet abc is negative 7.25 meters per second squared. If an object is thrown upward from an initial height of 70 meters with a velocity of 66 m/s find the following : velocity function, position function, velocity and position after 3 seconds, maximum height and velocity of object at impact with ground
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Position Function:
s(t) = 70 + 66t - 3.625t²
Velocity Function:
v(t) = 66 - 7.25t
State at 3 Seconds:
s(3) = 70 + 198 - 32.625 = 300.625 meters
v(3) = 66 -21.75 = 44.25 m/sec
Maximum Height:
v(t) = 66- 7.25t = 0
7.25t = 66
t ≈ 9.1 sec
s(9.1) ≈ 370.4 meters
Velocity at impact:
s(t) = 70 + 66t - 3.625t² = 0 : t > 0
t ≈ 19.2 second
v(19.2) ≈ -73.3 m/s
s(t) = 70 + 66t - 3.625t²
Velocity Function:
v(t) = 66 - 7.25t
State at 3 Seconds:
s(3) = 70 + 198 - 32.625 = 300.625 meters
v(3) = 66 -21.75 = 44.25 m/sec
Maximum Height:
v(t) = 66- 7.25t = 0
7.25t = 66
t ≈ 9.1 sec
s(9.1) ≈ 370.4 meters
Velocity at impact:
s(t) = 70 + 66t - 3.625t² = 0 : t > 0
t ≈ 19.2 second
v(19.2) ≈ -73.3 m/s