If an arrow is shot upward on the moon with a speed of 54 m/s, its height in met

Question

If an arrow is shot upward on the moon with a speed of 54 m/s, its height in meters t seconds later is given by
y = 54t 0.83t2.
(Round your answers to two decimal places.)
(a) Find the average speed over the given time intervals.

(ii)    [1, 1.5]

(iv)    [1, 1.01]

(v)    [1, 1.001]

The displacement (in centimeters) of a particle moving back and forth along a straight line is given by the equation of motion s = 4 sin t + 4 cos t, where t is measured in seconds. (Round your answers to two decimal places.)
(a) Find the average velocity during each time period.

(iii)    [1, 1.01]

(iv)    [1, 1.001]

Explanation / Answer

a) we have given y = 54t 0.83t2

let velocity v(t)=y'=54-2*( 0.83)t=54-1.66t

average speed for (ii)    [1, 1.5]

average speed=[v(1.5)-v(1)]/(1.5-1) =[(54-1.66*(1.5))-(54-1.66*(1))]/(0.5) =[51.51-52.34]/0.5 =-1.66 m/s

average speed for (iv)    [1, 1.01]

average speed =[v(1.01)-v(1)]/(1.01-1) =[(54-1.66*(1.01))-(54-1.66)]/0.01=[52.3234-52.34]/(0.01) =-1.66 m/s

average speed for (v)    [1, 1.001]

average speed =[v(1.001)-v(1)]/(1.001-1) =[(54-1.66*(1.001))-(54-1.66)]/(0.001)=[52.33834-52.34]/(0.001) =-1.66m/s

we have given s = 4 sin t + 4 cos t

first,we must recognise that average velocity is the change in distance/change in time

so average velocity for (iii) [1, 1.01]

average velocity = [s(1.01)-s(1)]/(1.01-1) =[(4 sin (*1.01) + 4 cos (*1.01))-(4 sin (*1) + 4 cos (*1))]/(0.01)

=[-4.12366927778+4]/(0.01) =-12.36 cm/sec

average velocity for (iv)    [1, 1.001]

average velocity=[s(1.001)-s(1)]/(1.001-1) =[(4 sin (*1.001) + 4 cos (*1.001))-(4 sin (*1) + 4 cos (*1))]/(0.001)

=[-4.01254661075+4]/(0.001) = -12.54 cm/sec

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