Question

1) A car is clocked at 25 m/s in a 50-mi/h zone. Is it speeding?

2) Use the definition of the meter to determine how far light travels in exactly 1 ns. Express your answer in meters to three significant figures.

3) Express a 85 mi/h speed limit in meters per second. Express your answer in meters per second.

4) GPS satellites complete approximately two full orbits each day. Express that rate in degrees per hour. Express your answer in degrees per hour.

5) One m/s is how many km/h? Express your answer in kilometers per hour to three significant figures.

6) Add 3.13105 m and 2.23103 km . Express your answer with the appropriate units.

Answer 1

1) 1 mile = 1609m

1 hour = 60*60 s = 3600s

Therefore it is speeding since the limit is 50 mi/h

2) Meter is defined as the distance taken by light in air or vacuum in exactly 1/299792458s

1ns=10^-9 s

Therefore distance travelled by light in 1ns is 299792458*10^-9m

That implies it travels a distance of 0.299792458m in 1ns

That implies it travels a distance of 0.300m in 1ns (3significant figures)

3)1 mile = 1609m

1 hour = 60*60 s = 3600s

4) GPS satellite completes 2 full orbit in a day

Rate = 2 orbits per day

=2 orbits/day

1 day = 24 hour

1 orbit means a complete circle

A circle has an angle of

Therefore 1 orbit =

5) 1km = 1000m

1h = 3600s

  (in 3 significant figures)

6) Number 1 = 3.13105 m

Number 2 = 2.23103 km

We can't add them since the units are not same

So we convert km to m and then add them together

So, Number 2 = 2.23103 km

=2.23103 *1000m

=2231.03 m

Therefore, Number 1+Number 2 =3.13105 m+2231.03 m

=2234.16105m

Since the number is greater than 1000 we convert it in km again

Therefore 2234.16105m = 2234.16105/1000km = 2.23416105m

Thus the sum of the two numbers are 2.23416105km