Free fall velocity

Free fall velocity

Pencil and paper
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Working with Students
Further Resources
This task is about using a formula to create a table, graph and using these to make a prediction.

The formula for the velocity with which an object hits the ground after free falling is

v = 10t

 

 v is the velocity in metres per second (m/s)
t is the free falling time in seconds (s)
 
a)
 
i)
 
 Use the formula to complete the table.
 
Time of free fall, t 0 1 2 3 4 5 6
Velocity, v 0            
 
 
ii)
 
  
Plot the points in the table above, and join them with a line.
 

Velocity of falling object


 
b)
In a car-safety demonstration, cars are dropped vertically from a crane.  
 
Emma counts 3.5 seconds between when a car is released and when it hits the ground.  
 
What is the velocity of the car when it hits the ground? __________ m/s
Task administration: 
This task is completed with pencil and paper only.
Level:
5
Curriculum info: 
Maths, Number and Algebra, Equations and expressions
Keywords: 
graph construction, linear equations, substitution, graph interpretation
Description of task: 
Students complete a table based on an algebraic formula for free fall velocity, plot the results, and interpret the graph.
Learning Progression Frameworks
This resource can provide evidence of learning associated with
Using symbols and expressions to think mathematically, sets 6-7
within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 
  Y10 (09/1998)
a)
i)
ii)
10, 20, 30, 40, 50, 60
Points plotted correctly, joined by a line.
[Accept if points not shown, but line drawn correctly.]
answer shown on graph
very easy
very easy
b)   35 easy
Next steps: 
Extension:(useful for class or group discussion)
A car manufacturer claims that the 'crumple-zone' in the front of a new car being tested will withstand a crash at 50 km/hour. Emma counts 1.5 seconds before the car hits the ground. Its crumple zone fails, and it gets smashed up. Is the manufacturer's claim valid? Give your working and reasons.
 
Answer:
Possibly, but the manufacturer must be given the benefit of the doubt. The car is travelling at 15 m/sec when it hits the ground. This is equivalent to 54 km/hour, which is just outside the allowed limit. [Calculation for conversion from m/sec to km/hr involves multiplication by 3600, then division by 1000.]