word problem

Question

A sprinter runs the 100 yd dash in 9.8 s . At this same rate, how long would it take the sprinter to run 100.0 m?

Express your answer using two significant figures. What is the sprinter's speed in meters per second? How long would it take the sprinter to run a distance of 1.80 km ?

Answer 1

Hey Amy,

 

 

1 yd = 0.9144 m

 

100 yds = 91.44 m

  9.8 s        9.8 S

 

(Ignore or forget the left side (yd/s)since you are looking for m/s)

 

9.33 m/s   --->   9.3 m/s (for 2 sig figs)

 

 

the sprinter's speed is 9.3 m/s

 

 

speed = distance / time   --->   speed * time = distance

 

distance / speed = time     100 (m) / 9.33 (m/s) = 10.72 seconds

 

10.72 seconds to complete 100m.  11 seconds for 2 sig figs.

 

 

11 seconds to complete 100m

 

 

1.80 km = 1800m

 

speed = distance / time   --->   speed * time = distance

 

distance / speed = time

 

1800 (m) / 9.33 (m/s) =  192.926 seconds --> 192.93 seconds --> 190 seconds for 2 sig figs.

 

 

 

190 seconds to complete 1.80 km (1800 m)

 

 

 

Good luck to you

 

 

Just a note:

192.93 seconds = 3 min 12.93 seconds   190 seconds = 3 min 10 seconds

Answer 2

Hi Amy,

D = 100 yds, t =9.8 s , V = D/t = 100/9.8 = 10.20 yd/sec is the speed

For d = 100 meters, convert the distance to yards, 1yd = 0.9144 m

d = 100 meters* 1 yd/0.9144 m = 109.36 yds

t = d/V = 109.36 yds/10.20yd/sec = 10.72

It will take the sprinter 10.72 seconds to run 100.0 meters.

The speed of the sprinter in meters per second is

V = (10.20 yds/sec)(0.9144m/1 yd) = 9.3 m/s

The time to run 1.80 km is

T = (1.80km *1000m/1km)/9.33m/s = 190 seconds

 

Note: I forgot that it is two significant figures