mechanics question (1 Viewer)

[cormglakes]

Hey how do I do part c?

a) Prove that the range on a horizontal plane of a particle projected upwards at an angle A to the plane with velocity V meters per second is (V²sin 2A)/g meters

A garden sprinkler sprays water symmetrically about its vertical axis at a constant speed of V meters per second. The initial direction of the spray varies continuously between angles of 15 and 60 degrees to the horizontal.
b) Prove that, from a fixed position O on level ground, the sprinkler will wet the surface of an annular region with center O and with internal and external radii V²/2g and V²/g meters respectively.
c) Deduce that, by locating the sprinkler appropriately relative to a rectangular garden bed of size 6 metres by 3 metres, the entire may be watered provided that (V²/2g) ≥ 1 + √(7)

 

[jimmysmith560]

This question was asked by Trebla back in 2006.

This was suggested:

draw two concentric circles and draw the rectangle in the annular region between the circles(rectangle side touching the circumference of the circle). construct a line from O to an edge of the rectangle(call it OX) and a perpendicular to the furthest edge of the rectangle(call the furthest edge XY)
thus let this point on furthest edge be D
OD^2=OX^2-XD^2 but entire bed will be wet if OD>=3+V^2/2g
(V^2/g)^2-9>=(3+V^2/2g)^2
solving gives V^2/2g>= root 7 +1

Another projectile motion question

Hi guys, I need just quick help with a part of this question: Prove that the range on a horizontal plane of a particle projected upwards at an angle A to the plane with velocity V metres per second is (V²sin 2A)/g metres A garden sprinkler sprays water symmetrically about its vertical axis...

boredofstudies.org

I hope this helps!

 

[idkkdi]

Hey how do I do part c?

a) Prove that the range on a horizontal plane of a particle projected upwards at an angle A to the plane with velocity V meters per second is (V²sin 2A)/g meters

A garden sprinkler sprays water symmetrically about its vertical axis at a constant speed of V meters per second. The initial direction of the spray varies continuously between angles of 15 and 60 degrees to the horizontal.
b) Prove that, from a fixed position O on level ground, the sprinkler will wet the surface of an annular region with center O and with internal and external radii V²/2g and V²/g meters respectively.
c) Deduce that, by locating the sprinkler appropriately relative to a rectangular garden bed of size 6 metres by 3 metres, the entire may be watered provided that (V²/2g) ≥ 1 + √(7)

when i did this,
i believe i had a circle and a rectangle inside it and you do some geometric constructions for part c.
wasn't too bad.

 

[idkkdi]

when i did this,
i believe i had a circle and a rectangle inside it and you do some geometric constructions for part c.
wasn't too bad.

actually i think there might have been two circles.