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A body is projected from a point O on horizontal ground with speed of 70 m/s. It passes through a point P, which is 45 m above the ground and 50 m horizontally from O.
i) Calculate the tangents of the two possible angles of elevation of the projected body.
♦ Friction is assumed zero. The only applicable force is gravity, which acts in the -K direction. Assume elevations are small such that gravity is constant at its surface value. The space of the flight will be an arbitrary OXZ plane.
This is a "Work in Progress."
Two independent events are in consideration. We call them Event-A and Event-B. Newton's Second Law and the physical conditions of the events are shown in the table.
Body-A | Body-B |
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The "domain of time" for Body-A commences at the time t = 0+. We use the notation "zero-positive" to mean the instant after the event commenced. The last time of interest of Body-A is t = tp,A. This time is not known This is that instance Body-A arrives at the position P.
The above equation sets show only one difference, the angle of elevation upon launch." We will work on Set-A. The table below shows and explains the steps.
(i)
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(ii)
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(iii) Both integrals of step (ii) have "1" as integrand. The differentials of such integrals are called "exact." (If the integrand is "1", the integral gets a special, but needless title ~ exact). Such integrals integrate
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(iv)
The above result can be made more specific. We know the initial speed (V(t=0+) and we have identified the launch angle as θ1. Enter these into the above equations. Finally, for this phase, write our result along with the special position given us: |
A body is projected from a point O on horizontal ground with speed of 70 m/s. It passes through a point P, which is 45 m above the ground and 50 m horizontally from O. Calculate the tangents of the two possible angles of elevation of the projected body. Find also the gradients at P of the two paths.
Premise presently unwritted!