1. A projectile of mass m is launched from the surface of the earth directly upward with initial speed . Neglecting air resistance, its velocity v(t) satisfies the differential equation dv m-mg where g is the acceleration due to gravity, a constant. Solve the differential equation subject to initial condition (0), where up is a positive number, to discover - (a) The velocity at any time t seconds after launching the projectile expressed in terms of g and to; (b) The height of projectile at any time t; (e) The maximum height So reached by the projectile expressed in terms of g and to.
1. A projectile of mass m is launched from the surface of the earth directly upward with initial speed . Neglecting air resistance, its velocity v(t) satisfies the differential equation dv m-mg where g is the acceleration due to gravity, a constant. Solve the differential equation subject to initial condition (0), where up is a positive number, to discover - (a) The velocity at any time t seconds after launching the projectile expressed in terms of g and to; (b) The height of projectile at any time t; (e) The maximum height So reached by the projectile expressed in terms of g and to.
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
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Transcribed Image Text:1. A projectile of mass m is launched from the surface of the earth directly upward
with initial speed . Neglecting air resistance, its velocity v(t) satisfies the
differential equation
dv
m-mg
where g is the acceleration due to gravity, a constant. Solve the differential
equation subject to initial condition (0), where up is a positive number, to
discover
-
(a) The velocity at any time t seconds after launching the projectile expressed
in terms of g and to;
(b) The height of projectile at any time t;
(e) The maximum height So reached by the projectile expressed in terms of g
and to.
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