jane is a 45 kg cyclist. If her bike weighs 100 N and she landed with her bike on the floor at a vertical reaction force of 890 N, what was her vertical acceleration during landing?
To find Jane's vertical acceleration during landing, we need to use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration. The formula is as follows:
F_net = m * a
In this case, the only force acting on Jane and her bike during landing is the vertical reaction force, which is equal to 890 N. So, the net force acting on Jane and her bike is 890 N.
Now, we know that the combined mass of Jane and her bike is equal to the mass of Jane (45 kg) plus the weight of the bike (100 N). To convert the weight of the bike to mass, we divide it by the acceleration due to gravity (which is approximately 9.8 m/s^2), using the formula:
Weight = mass * acceleration due to gravity
100 N = bike mass * 9.8 m/s^2
bike mass = 100 N / 9.8 m/s^2 ≈ 10.2 kg
Therefore, the combined mass of Jane and her bike is 45 kg + 10.2 kg = 55.2 kg.
Using Newton's second law, we can now find the vertical acceleration:
F_net = m * a
890 N = 55.2 kg * a
Rearranging the equation to solve for acceleration (a), we have:
a = F_net / m
a = 890 N / 55.2 kg ≈ 16.1 m/s^2
Therefore, Jane's vertical acceleration during landing was approximately 16.1 m/s^2.