. Differential and integral calculus, an introductory course for colleges and engineering schools. er return is milesper second. 2. Find the percentage of error introduced by using formula (4) insteadof formula (3) when h has the value (a) 100 miles, (b) 1 mile, (c) 100 feet. 3. With what velocity and in what time would a body reach the earthfalling from a distance R above the surface? from a distance 100,000 milesabove the surface? 4. What is the vertical velocity that a projectile fired from the surfaceof the moon would have to have in order that it should never return?Assume the moons
. Differential and integral calculus, an introductory course for colleges and engineering schools. er return is milesper second. 2. Find the percentage of error introduced by using formula (4) insteadof formula (3) when h has the value (a) 100 miles, (b) 1 mile, (c) 100 feet. 3. With what velocity and in what time would a body reach the earthfalling from a distance R above the surface? from a distance 100,000 milesabove the surface? 4. What is the vertical velocity that a projectile fired from the surfaceof the moon would have to have in order that it should never return?Assume the moons radius to be 1080 miles, and gravity on its surfaceto be feet per second. 5. With what velocity and in what time would a body reach the moonfalling from a distance of 10,800 miles above the surface, the attractionof the earth being neglected? 153. The Motion of a Projectile. Problem 1. A particle is projected from a fixed point O on the earthssurface, with a velocity v0, in a direction that makes an angle 4> with thehorizontal. Determine the motion, neglecting the resistance of the 216 INTEGRAL CALCULUS §153 Solution. The particle will of course remain in the same vertical planethroughout its flight; it will rise for a time, and will finally be broughtback to the earth by the action of gravitation. Let 0 be the origin and let the axes be the horizontal and ver-tical lines through 0 that He in thevertical plane. Let P, with the co-ordinates x and y, be the particlesposition t units of time after the be-ginning of the flight. If gravitationdid not act, the body would move ina straight line with the constant ve-locity v0, and the horizontal and ver-tical components of the velocity at any time t would have respectively theconstant values v0 cos and vQ sin 4>. But gravitation engenders a velocitycomponent downward of gt. Hence the velocity components of the par-ticle at P are ri\ dx dy • , . (1) — = v0 cos , -f- = v0 sin - at Integrating these equations, w
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