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 can 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. In this case, the net force is the difference between the vertical reaction force and the weight of both Jane and her bike.
Let's break down the problem step by step:
1. Find the weight of Jane:
The weight of an object can be calculated using the equation weight = mass * gravity, where gravity is approximately 9.8 m/s² on Earth. In this case, Jane's weight is equal to 45 kg * 9.8 m/s².
weight of Jane = 45 kg * 9.8 m/s²
2. Find the total weight of Jane and her bike:
Since the weight of the bike is 100 N, the total weight becomes the sum of Jane's weight and the weight of the bike.
total weight = weight of Jane + weight of bike
3. Calculate the net force:
The net force acting on Jane during the landing is equal to the vertical reaction force minus the total weight of Jane and her bike.
net force = vertical reaction force - total weight
4. Calculate the acceleration:
Using Newton's second law of motion, we can rearrange the formula to calculate the acceleration:
net force = mass * acceleration
Rearranging the formula to solve for acceleration, we get:
acceleration = net force / mass
Now, plug in the values we calculated earlier to find Jane's vertical acceleration during landing:
acceleration = net force / (mass of Jane + mass of bike)
By substituting the values from steps 1, 2, and 3, the formula becomes:
acceleration = (vertical reaction force - total weight) / (mass of Jane + mass of bike)
Now, you can calculate the vertical acceleration by substituting the known values into the formula and performing the calculations.