This homework was assigned Week 4 Block 2 by Dr. Rickert and is due by

5PM
Wednesday, September 29, 1999
.
** **

**Exercises 1 and 2**

A bowling ball is thrown upwards from a height of 70.000 meters with an initial velocity of 25.000 meters per second upwards. 1 (A) Determine the velocity function of the bowling ball.

1 (B) Determine the height function of the bowling ball.

2 (A) Plot the height function of the bowling ball and estimate the time that the bowling ball reaches its maximum height. What is this maximum height?

2 (B) With what velocity does the bowling ball hit the ground?

`> `
**restart;**

`> `
**st := t -> 70+25*t-4.9*t^2;**

`> `
**vt := diff(st(t),t);**

`> `
**plot(st(t),t=2.54..2.56);**

The bowling ball reaches a maximum height of 101.888 m after 2.551 seconds.

`> `
**tEnd := fsolve( st(t)=0,t=0..8);**

`> `
**subs(t=tEnd,vt);**

`> `

**Exercise 3**

A mass on a spring experiences an acceleration of
meters per second per second.

The initial velocity of the mass is
/5 meters per second. The intitial position of the mass is +1 meter.

3 (A) Determine the velocity function of the mass.

3 (B) Determine the position function of the mass.

`> `
**restart;**

`> `
**at := 8*cos(5*t-Pi/4);**

`> `
**vt := int(at,t)+c;**

`> `
**vt := subs( subs(t=0,vt) = -4*sqrt(2/5) ,c );**

`> `

`> `
**st := int(vt,t)+c;**

`> `
**st := subs(c=1,st);**

`> `
**vt := solve(**

`> `

`> `

**Exercise 4**

The position function (in meters) of a mass attached to a spring is given below.
*t*
is in seconds.

`> `

4(A) Create a model for the position function that matches the given information.

4(B) using this model, determine the velocity and acceleration functions for the mass.

4(C) At what time is the acceleration maximized?

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