A cyclist whose mass is 48 kg turns a corner with a radius of 30 m at a speed of 25 m/s.


A) What is the magnitude of the cyclist's acceleration?
B) what is the magnitude of the force action on the cyclist?

To find the magnitude of the cyclist's acceleration, we can use the centripetal acceleration formula:

a = v^2 / r

where:
a = acceleration
v = velocity
r = radius of the corner

Given:
v = 25 m/s
r = 30 m

Using the formula, we can calculate the magnitude of the cyclist's acceleration:

a = (25^2) / 30
a = 625 / 30
a ≈ 20.83 m/s^2

Therefore, the magnitude of the cyclist's acceleration is approximately 20.83 m/s^2.

To find the magnitude of the force acting on the cyclist, we can use the formula for centripetal force:

F = m * a

where:
F = force
m = mass
a = acceleration (which we calculated in part A)

Given:
m = 48 kg
a ≈ 20.83 m/s^2

Using the formula, we can calculate the magnitude of the force acting on the cyclist:

F = 48 * 20.83
F ≈ 999.84 N

Therefore, the magnitude of the force acting on the cyclist is approximately 999.84 N.