Question

Jason takes off from rest across level water on his jet-powered skis. The combined mass of Jason and his skis is 75 kg (the mass of the fuel is negligible). The skis have a thrust of 200 N and a coefficient of kinetic friction on water of 0.10. Unfortunately, the skis run out of fuel after only 17 s. How far has Jason traveled when he finally coasts to a stop?A.) 250 mB.) 350 mC.) 490 mD.) 660 m

Answer 1

Option D

660 m

Step-by-step explanation:

ma=Thrust – friction where m is mass and a is acceleration

ma=200 - \mu mg

Substituting m for 75 kg,
`\mu` for 0.10, g for 9.81

75a=200 - 0.10*75*9.81

75a= 200-73.575

a=126.425/75

`a = 1.685667 m/s^(2)`

For the first 17 seconds

Velocity v = a*t = 1.685667 17 = 28.65633 m/s

Distance =
`0.5*a*t^(2) = 0.5*1.685667*17^(2)` = 243.5788 m

After fuel is over

Force acting is only friction

`F = ma = -\mu mg` since m are common

`a = -\mu g = -0.1*9.81 = -0.981 m/s^(2)`

`v^(2) - u^(2) = 2as`

Where v is final velocity which is zero because after running out of fuel, skis come to rest. U is initial velocity which is 28.65633 m/s

`0 - 28.65633^(2) = 2*-0.981*s`

s = 418.5450765 m

Total distance = s1+s2 = 243.5788 m + 418.5450765 m m = 662.1239098 m

Distance covered is approximately 660 m