Questions 9 and 10 please. d dropped. Both stones vertically downward 1.o 44m ab

Question

Questions 9 and 10 please.

d dropped. Both stones vertically downward 1.o 44m above the water. initial velocity strike the water s after the first was of the second at the same time. What was the stone? 9. A confused cowfolk at the Lethbridge Stampede travels the following line segments 60om[E], 40omIN], 300m (E40°N] & 700mis60 If the total time was 2.0h, calculate a) the average velocity b) the average speed 10. A pilot wishes of El in 45 min. On with the meteorological office, she finds that there will be a wind of 80km/h from the north for the entire flight. What heading and airspeed must she use for the flight?

Explanation / Answer

Q9.

let north be along +ve y axis and east be along +ve x axis.

let i and j are unit vectors along +ve x and +vey axis.

total displacement

=600 i + 400 j +300*(sin(40) i+ cos(40) j)+700*(-cos(60) i -sin(60) j)

=(600+300*sin(40)-700*cos(60)) i + (400+300*cos(40)-700*sin(60)) j

=442.84 i + 23.596 j

part a:

average velocity=magnitude of total dispalcement/total time

=sqrt(442.84^2+23.596^2) m/(2*3600 seconds)

=0.061593 m/s

part b:

average speed=total distance/total time

=(600+400+300+700)/(2*3600) m/s

=0.27778 m/s

Q10.

let north be along +ve y axis and east be along +ve x axis.

let i and j are unit vectors along +ve x and +vey axis.

let her speed be v km/hr and angle with +ve x axis be theta.

her velocity w.r.t wind=v*(cos(theta) i + sin(theta) j)

velocity of wind w.r.t. ground=(80 km/hr) j

so velocity of the plane =velocity of plane w.r.t. wind + velocity of win w.r.t. ground

=v*cos(theta) i + (v*sin(theta)+80) j

as the direction of total velocity is 45 degree north of east

velocity along +ve x and +ve y axis should be equal.

v*cos(theta)=v*sin(theta)+80...(1)

total velocity can be written as

v*cos(theta)*(i+j)

speed=sqrt(2)*v*cos(theta)

given that speed=300 km/45 minutes

=400 km/hr

hence sqrt(2)*v*cos(theta)=400

==>v*cos(theta)=282.84 km/hr...(2)

using equation 2 in equation 1:

v*sin(theta)+80=282.84

==>v*sin(theta)=202.84....(3)

divding equation 2 by equation 3:

cot(theta)=282.84/202.84

==>theta=35.646 degrees

using the value of theta in equation 2, we get v=348 km/hr

so her speed should be 348 km/hr and direction 35.646 degree north of east.

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