To show that the isoclines of d y d t = t are vertical lines and sketch the slope field for − 2 ≤ t ≤ 2 , − 2 ≤ y ≤ 2 and plot the integral curves passing through ( 0 , − 1 ) and ( 0 , 1 )

Question

A body of mass m at the top of a 100 m high tower is thrown vertically upward with an initial velocity of 10 m/s. Assume that the air resistance FD acting on the body is proportional to the velocity V, so that FD=kV. Taking g = 9.75 m/s2 and k/m = 5 s, determine: a) what height the body will reach at the top of the tower, b) how long it will take the body to touch the ground, and c) the velocity of the body when it touches the ground.

Answer 1

Question

Chapter 9.3, Problem 9E

To determine

To show that the isoclines of $\frac{d y}{d t} = t$ are vertical lines and sketch the slope field for $- 2 \leq t \leq 2, - 2 \leq y \leq 2$ and plot the integral curves passing through $(0, - 1)$ and $(0, 1)$

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