Chapter 6.1, Problem 26E

(a)

To determine

The upper estimate for the speed when t=5 using LRAM₅

Answer to Problem 26E

The upper estimate for the speed when t=5 using LRAM₅ is $S_5=74.65\text{ft/sec}$

Explanation of Solution

Given information:

  

Formula used:

The left-hand point rectangle approximation method (LRAM) is used.

Calculation:

For left-hand point rectangle approximation method (LRAM), area is divided into rectangles. Total time is divided into equal intervals and at left-hand point of interval calculates the velocity which is equal to height of rectangle then calculates the area or small rectangles then adds all the area. Total area gives the Speed. There is no need to measure height because we have recorded data.

Use LRAM with 5 equal subintervals. Take the value at left-end point of interval and add all the values then multiply with the length of subinterval which is unity.

  $\begin{array}{l}{S}_5=1\left[32+19.41+11.77+7.14+4.33\right]\\ S_5=74.65\text{ft/sec}\end{array}$

Conclusion:

The upper estimate for the speed when t=5 using LRAM₅ is $S_5=74.65\text{ft/sec}$

(a)

To determine

The lower estimate for the speed when t=5 using RRAM₅

Answer to Problem 26E

The lower estimate for the speed when t=5 using RRAM₅ is $S_5=45.28\text{ ft/sec}$

Explanation of Solution

Given information:

  

Formula used:

The right-hand point rectangle approximation method (RRAM) is used.

< p>Calculation:

For right-hand point rectangle approximation method (RRAM), area is divided into rectangles. Total time is divided into equal intervals and at right-hand point of interval calculates the velocity which is equal to height of rectangle then calculates the area or small rectangles then adds all the area. Total area gives the Speed. There is no need to measure height because we have recorded data.

Use RRAM with 5 equal subintervals. Take the value at right-end point of interval and add all the values then multiply with the length of subinterval which is unity.

  $\begin{array}{l}{S}_5=1\left[19.14+11.77+7.14+4.33+2.63\right]\\ S_5=45.28\text{ ft/sec}\end{array}$

Conclusion:

The lower estimate for the speed when t=5 using RRAM₅ is $S_5=45.28\text{ ft/sec}$

(c)

To determine

The upper estimate for the distance fallen when t=3.

Answer to Problem 26E

The distance fallen up to 3 second is 146.59 feet

Explanation of Solution

Given information:

  

Formula used:

The upper estimate formula is used.

Calculation:

Upper estimate for first second

  $\text{speed}=32.00\text{ft/sec}$

Upper estimate for next second

  $\begin{array}{l}\text{speed}=\left(32.00+19.41\right)\text{ft/sec}\\ \text{speed}=51.41\text{ft/sec}\end{array}$

Upper estimate for third second

  $\begin{array}{l}\text{speed}=\left(32.00+19.41+11.77\right)\text{ft/sec}\\ \text{speed}=63.18\text{ft/sec}\end{array}$

So,

Upper estimate for the distance fallen up to 3 second

  $\begin{array}{l}\text{distance}=32+51.41+63.18\\ \text{distance}=146.59\text{feet}\end{array}$

Conclusion:

The distance fallen up to 3 second is 146.59 feet