By law, a wheelchair service ramp may be inclined no more than `4.76^(@)`. If the base of a ramp begins 15 feet from the base of a public building, which equation could be used to determine the maximum height, h, of the ramp where it reaches the building's entrance?

A lighthouse is built on the edge of a cliff near the ocean, as shown in the diagram above. From a boat located 200 feet from the base of the cliff, the angle of elevation to the top of the cliff is 18^(@) and the angle of elevation to the top of the lighthouse is 28^(@) . Which of the following equations could be used to find the height of the lighthouse, x, in feet?

An object A is dropped from the top of a 30m high building and at the same moment another object B is projected vertically upward with an initial speed of 15m//s from the base of the building. Mass of the object A is 2kg while mass of the object B is 4kg . Find the maximum height above the ground level attained by the centre of mass of A and B system (take g=10m//s^2 )

(i) A non uniform cube of side length a is kept inside a container as shown in the figure. The average density of the material of the cube is 2 rho where rho is the density of water. Water is gradually fille din the container. It is observed that the cube begins to topple, about its edge into the plane of the figure passing through pointA, when the height of the water in the container becomes (a)/(2) . Find the distance of the centre of mass of the cube from the face AB of the cube. Assume that water seeps under the cube. (ii) A rectangular concrete block (specific gravity =2.5) is used as a retatining wall in a reservoir of water. The height and width of the block are x and y respectively the height of water in the reservoir is z=(3)/(4)x . the concrete block cannot slide on the horizontal base but can rotate about an axis perpendicular to the plane of the figure and passing through point A (a) Calculate the minimum value of the ratio (y)/(x) for which the block will not begin to overturn about A. (b) Redo the above problem for the case when there is a seepage and a thin film of water is present under the block. Assume that a seal at A prevents the water from flowing out underneath the block.

Carlos and Katherine are estimating acceleration by rolling a ball from rest down a ramp. At 1 second, the ball is moving at 5 meters per second m/s, at 2 seconds, the ball is moving at 10 m/s, at 3 seconds, the ball is moving at 15m/s, and at 4 seconds, it is moving at 20m/s. When graphed on an xy-plane, which equation best describes the ball's estimated acceleration where y expresses speed and x ecpresses time?

Carlos and Katherine are estimating acceleration by rolling a ball from rest down a ramp. At 1 second, the ball is moving at 5 meters per second (m/s), at 2 seconds, the ball is moving at 10 m/s, at 3 seconds, the ball is moving at 15 m/s, and at 4 seconds, it is moving at 20 m/s. When graphed on an xy-plane, which equation best describes the ball's estimated acceleration where y expresses speed and x expresses time?

A student performs an experiment to determine how the range of a ball depends on the velocity with which it is projected. The "range" is the distance between the points where the ball lends and from where it was projected, assuming it lands at the same height from which it was projected. It each trial, the student uses the same baseball, and launches it at the same angle. Table shows the experimental results. |{:("Trail","Launch speed" (m//s),"Range"(m)),(1,10,8),(2,20,31.8),(3,30,70.7),(4,40,122.5):}| Based on this data, the student then hypothesizes that the range, R, depends on the initial speed v_(0) according to the following equation : R=Cv_(0)^(n) , where C is a constant and n is another constant. Based on this data, the best guess for the value of n is :-