a) K-3 Solve the differential equation a = kyx using the method of separation of variables. dy dx b) 3 Discuss the difference between the direction fields of the differential equations dy=kyx and dy dx = = -kyx. How the sign of the coefficient affects the solution curves. A racquetball is hit straight upward with an initial velocity of v₁ = km/s. The mass of a racquetball is m=0.05kg. Air resistance acts on the ball with a force numerically equal to Air resistance acts on the ball with a force numerically equal to 0.5v, where v represents the velocity of the ball at time t. To find the velocity of the ball as a function of time and evaluate time for the ball to reach its maximum height w can solve initial value problem using the firs order linear DE such as dv m dt == −0.5v — m(9.8), v₁ = k ← k=3 Rewrite the equation as a standard form of a linear DE. Find the integration factor. d) k= 3 Sketch the direction field of the equation from part c) both manually and by using software. Explain the relation between the solution curves and the direction field. K= 3 Find the velocity of the ball as a function of time. How long does it take for the ball to reach its maximum height?

a) K-3 Solve the differential equation a = kyx using the method of separation of variables. dy dx b) 3 Discuss the difference between the direction fields of the differential equations dy=kyx and dy dx = = -kyx. How the sign of the coefficient affects the solution curves. A racquetball is hit straight upward with an initial velocity of v₁ = km/s. The mass of a racquetball is m=0.05kg. Air resistance acts on the ball with a force numerically equal to Air resistance acts on the ball with a force numerically equal to 0.5v, where v represents the velocity of the ball at time t. To find the velocity of the ball as a function of time and evaluate time for the ball to reach its maximum height w can solve initial value problem using the firs order linear DE such as dv m dt == −0.5v — m(9.8), v₁ = k ← k=3 Rewrite the equation as a standard form of a linear DE. Find the integration factor. d) k= 3 Sketch the direction field of the equation from part c) both manually and by using software. Explain the relation between the solution curves and the direction field. K= 3 Find the velocity of the ball as a function of time. How long does it take for the ball to reach its maximum height?

College Algebra

10th Edition

ISBN:9781337282291

Author:Ron Larson

Publisher:Ron Larson

Chapter3: Polynomial Functions

Section3.5: Mathematical Modeling And Variation

Problem 7ECP: The kinetic energy E of an object varies jointly with the object’s mass m and the square of the...

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