Diving board

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Don Shearman

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From users who are not members of MfEP Progress Quizzes :

Terry Young

said

Ready to use

6 months, 3 weeks ago

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Terry Young 6 months, 3 weeks ago

Gave some feedback: Ready to use

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Don Shearman 1 year ago

Published this.

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Don Shearman 2 years, 1 month ago

Created this.

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Question statement

Give any introductory information the student needs.

			Name	Type	Generated Value

height	number	10
velocity	number	3.4
time	number	1.82
negRoot	number	-1.12

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(1.5..10 #0.5)

JME function reference

Description

height of diving board above the water

Describe what this variable represents, and list any assumptions made about its value.

Can an exam override the value of this variable?

Generated value: `number`

→ Used by:

negRoot
time

This variable doesn't seem to be used anywhere.

Parts

Gap-fill
1. Gap Number entry
  Add

Gap-fill

Ask the student a question, and give any hints about how they should answer this part.

A diver jumps off a diving board $\var{height}$ metres above the water with an initial vertical velocity of $\var{velocity}$ m/s. The diver's height above the water is given by

$h(t)=\simplify{-4.9t^2+{velocity}t+{height}} \text{ metres}$

How long does it take for the diver to hit the water? (Give your answer correct to 2 decimal places)

It takes Unnamed gap seconds to hit the water. Show full working on your handwritten notes.

Advice

We are given that the divers height above the water at time $t$ is given by

$h(t)=\simplify{-4.9t^2+{velocity}t+{height}} \text{ metres.}$

Since the surface of the water will be at height $h(t)=0$ we need to solve

$\simplify{-4.9t^2+{velocity}t+{height}}=0.$

To do this we use the quadratic formula giving us

$\begin{align}t&=\frac{-\var{velocity}\pm\sqrt{\var{velocity}^2+4\times\var{height}\times 4.9}}{-2\times 4.9}\\&=\frac{-\var{velocity}\pm\sqrt{\var{velocity^2+4*height*4.9}}}{-9.8}\\&\approx \var{time}\text{ or }\var{negRoot}\end{align}$

Since time needs to be a positive quantity for the solution to make sense we can dismiss the negative root and conclude that it takes $\var{time}$ seconds for the diver to hit the water.

Give a worked solution to the whole question.

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Part	Test	Passed?
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Number entry
Number entry		Hasn't run yet

This question is used in the following exams:

Class Test 1 by Don Shearman in MfEP Progress Quizzes.
NCM4 TEST Regression Modeling Basics by Terry Young in Terry's workspace.

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Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

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Checkpoint description

Terry Young 6 months, 3 weeks ago

Don Shearman 1 year ago

Don Shearman 2 years, 1 month ago

Error in variable testing condition

Error

Warning

Generated value: `number`

Parts

Gap-fill

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Error

Diving board

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Terry Young 6 months, 3 weeks ago

Don Shearman 1 year ago

Don Shearman 2 years, 1 month ago

Error in variable testing condition

Error

Warning

Generated value: number

Parts

Gap-fill

Generated value: `number`