Question

An airplane is flying in a horizontal circle of radius 1.5 km with a speed of 450 km/h. What is the magnitude of the centripetal acceleration of the plane?

Answer 1

`a_c=10.4` `ms^-2`

Explanation:

v = 450 km/h=`450*5/18=125` m/s
r=1.5km = 1.5*1000 = 1500 m
centripetal acceleration`(a_c)=v^2/r`
`a_c=15625/1500=10.4` `ms^-2`

Answer 2

The magnitude of the centripetal acceleration is `10.4 m/s^2`r.

Explanation:

The formula for centripetal acceleration, `a_c`, is

`a_c = v^2/r`

Before using that, we should convert the units of our data to the standard m for the radius and m/s for the velocity.

`r = 1.5 cancel(km) * (1000 m)/(1 cancel(km)) = 1500 m`

`v = 450 cancel(km)/cancel(hr) * (1000 m)/(1 cancel(km)) * (1 cancel(hr))/(3600 s) = 125 m/s`

Going back to the formula for centripetal acceleration

`a_c = v^2/r = (125 m/s)^2/(1500 m) = (15625 m^2/s^2)/(1500 m) = 10.4 m/s^2`
(I tried to show cancelling of one of the meters in the numerator with the meter in the denominator. I could not make the formatter show that.)

I hope this helps,
Steve