Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

You are not logged in.

- Topics: Active | Unanswered

Pages: **1**

**295Ja****Member**- Registered: 2012-07-28
- Posts: 39

Hi! Help please.

Problem 1:

A ball was thrown downward from the top of a building at a speed of 10 meters per

second and it hit the ground 3 seconds later. How tall was the building? [Note: Use

-10 m/s² for acceleration due to gravity.]

>>Here's what I think I should do:

1. Find the velocity then position functions

Here's what I got:

Velocity Function:

v(t)=-10t+C*

Position Function:

s(t)=-5t²+C*t+C**

[Note: C*=constant after integrating a(t) and C**= constant after integrating v(t)]

2.Find the value of C* and C**

My question: is it right to use these: v(3)=0 and s(3)=0 to find them?

3.Evaluate s(0)-s(3)

Problem 2

The base of a solid S is the region bounded by y =square root of (16-x²) and the x-axis, and each

cross-section perpendicular to the x-axis is an isosceles right triangle having one leg on

the base of S. Using the method of slicing, determine the volume of S.

>>I have a hard time with this problem. A help on visualizing the figure and/or setting-up the integral that will give the volume would do.

Thank you!

Offline

**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 7,925

hi 295Ja

Q1. You can use

directly, where g = 10 t = 3 and u = 10

This assumes s(0) = 0

Q2 The picture below is my view of this problem.

On the left we have the graph of the function for the base.

On the right a 3D represenation of the base with one slice shown rising up in a third dimension.

The slice has area half y^2 and thickness dx

So integrate these to get the volume.

Bob

Children are not defined by school ...........The Fonz

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

Offline

**295Ja****Member**- Registered: 2012-07-28
- Posts: 39

Thanks bob bundy!

In Q1,using integration, I got the same answer as when I plugged in the values in the position function you gave but could you still

check my solution for any flaw?

Here it is:

v(t)=-10t+C*

s(t)=-5t²+C*t+C**

Given that speed=10 and since speed=absolute value of velocity, v=-10

v(0)=-10t+C*=-10

C*=-10

s(t)=-5t²-10t+C**

but s(3)=0

C**=75

s(t)=-5t²-10t+75

s(0)-s(3)=75

Offline

**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 7,925

75 is what I make it too.

Bob

Children are not defined by school ...........The Fonz

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

Offline

Pages: **1**