1D Kinematics Legacy Problem #4 Guided Solution
Problem*
In last week's Homecoming victory, Al Konfurance, the star halfback of South's football team, broke a tackle at the line of scrimmage and darted up field untouched. He averaged \(\units{9.8}{\unitfrac{m}{s}}\) for an 80-yard (73 m) score. Determine the time for Al to run from the line of scrimmage to the end zone.
Audio Guided Solution
A successful solution to a physics problem often involves more than what meets the eye. More than merely plugging in numbers to a calculator and cranking out an answer, a problem often involves careful reading and attention to some details. In here we're told that our all-star halfback is moving 80 yards, or 73 meters, at a speed of 9.8 meters per second. Now the fact that the distance is given in two sets of units means that we're going to have to give some attention to these two numbers. The 80 yards and the 73 meters are equivalent to one another, but expressed in different units. And the quantity that we're interested in is the 73 meters, because the average speed is given in 9.8 meters per second. If I'm reading this problem and failing to give proper attention to the units, I'm certainly going to miss that little detail. Now that I know that I have a distance and I have an average speed, I can think in terms of what equations I have that relate these two quantities to the requested quantity, the time. And that equation is that the average speed is the distance divided by the time. To solve for time, I have to plug my numbers, 9.8 meters per second, into the equation on the side of average speed, and I have to put my 73 meters into the numerator. So I now have 9.8 equal 73 divided by t, and I have to solve for t. This involves proper algebra skills. You need to multiply both sides of the equation by t, and you have 9.8 times t equals 73. And now you can divide through by 9.8, and you have your answer.
Solution
7.4 s
Habbits of an Effective Problem Solver
- Read the problem carefully and develop a mental picture of the physical situation. If necessary, sketch a simple diagram of the physical situation to help you visualize it.
- Identify the known and unknown quantities in an organized manner. Equate given values to the symbols used to represent the corresponding quantity - e.g., \(v_o = \units{0}{\unitfrac{m}{s}}\); \(a = \units{4.2}{\unitfrac{m}{s^2}}\); \(v_f = \units{22.9}{\unitfrac{m}{s}}\); \(d = \colorbox{gray}{Unknown}\).
- Use physics formulas and conceptual reasoning to plot a strategy for solving for the unknown quantity.
- Identify the appropriate formula(s) to use.
- Perform substitutions and algebraic manipulations in order to solve for the unknown quantity.
Read About It!
Get more information on the topic of 1D Kinematics at The Physics Classroom Tutorial.