A ball is kicked from the horizontal ground with an initial velocity of 40 m/s at an angle of 28 degrees to the horizontal. Calculate the initial horizontal component Vh as well as the time is taken to reach the maximum height above the ground.
Horizontal component (Vh) = Vcosx Vh = (40)(cos28) Vh = 35.32 m/s Vertical component = Vsinx = (40)(sin28) = 18.78 m/s Therefore using v = u + at V = 0 (at the max height) U = 18.78 (initial vertical velocity) a = -9.81 (deceleration due to gravity) t = unknown variable 0 = 18.78 + (-9.81)t 9.81t = 18.78 t = 1.91s to reach the maximum height
The length of a rectangular field is 7/5 its width. If the perimeter of the field is 450 meters, what are the length and width of the field?
Let length = x Let width = y x = 7/5y Perimeter = 2x + 2y BUT x = 7/5y So P = 2(7/5y) + 2y 450 = 14/5y + 10/5y 450 = 24/5y y = 93.75m (width) Therefore x = 7/5(93.75) = 131.25m (length)
A uniform beam PQ is balanced on a pivot. The length of the beam is 3.0m and its weight is 50N. The beam is supported on a pivot 1.0m from end P. A load of weight W is hung from end P and the beam is in equilibrium. What is the value of W?
For equilibrium, all clockwise moments must equal all anti-clockwise moments. Moment = Force x perpendicular distance from pivot Clockwise moments = Weight of bar x 0.5m (halfway) Therefore = 50 x 0.5 Anti clockwise moments = W x 1 Therefore: 50 x 0.5 = W x 1 W = 25N The weight hung from end P is 25N