Step-by-step explanation:
To find the magnitudes of the cyclist's radial and tangential accelerations when his speed is 10 m/s, we can use the equations for radial and tangential acceleration:
Radial acceleration: ar = v^2 / r
Tangential acceleration: at = a - ar
where ar is the radial acceleration, at is the tangential acceleration, v is the speed, r is the radius of the curve, and a is the acceleration (in this case, the deceleration of 0.5 m/s^2).
Plugging in the values given in the problem, we get:
ar = (10 m/s)^2 / (30 m) = 0.33 m/s^2
at = (-0.5 m/s^2) - (0.33 m/s^2) = -0.83 m/s^2
Therefore, the magnitude of the radial acceleration is 0.33 m/s^2, and the magnitude of the tangential acceleration is -0.83 m/s^2.
Note that the negative sign on the tangential acceleration indicates that it is directed opposite to the velocity, which is consistent with the fact that the cyclist is decelerating.