A sprinter is pushing against the starting blocks with one foot with a backward horizontal force of 650 N and a downward vertical force of 900 N. What is the resultant force generated by the sprinter?
Question
A sprinter is pushing against the starting blocks with one foot with a backward horizontal force of 650 N and a downward vertical force of 900 N. What is the resultant force generated by the sprinter?
Solution
To find the resultant force, we can use the Pythagorean theorem because the forces are at right angles to each other. The Pythagorean theorem is a² + b² = c², where c is the hypotenuse of a right-angled triangle and a and b are the other two sides.
Step 1: Identify the forces. The horizontal force (a) is 650 N and the vertical force (b) is 900 N.
Step 2: Square both forces. (650 N)² = 422500 N² and (900 N)² = 810000 N².
Step 3: Add the squared forces together. 422500 N² + 810000 N² = 1232500 N².
Step 4: Take the square root of the sum to find the resultant force (c). The square root of 1232500 N² is approximately 1110 N.
So, the resultant force generated by the sprinter is approximately 1110 N.
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