Finding Speed on an incline when Power is known.

[ddn87]

Homework Statement

A car of weight 1920 N operating at a rate of
107 kW develops a maximum speed of 41 m/s
on a level, horizontal road.
Assuming that the resistive force (due to
friction and air resistance) remains constant,
what is the car’s maximum speed on an incline
of 1 in 20; i.e., if θ is the angle of the incline
with the horizontal, sin θ = 1/20 ?
Answer in units of m/s.

Homework Equations

This is the equation that i believe we have to use.
P=F x V

The Attempt at a Solution

So we have 107 kW which i assume i have to change to 107000 W.

Then we do 107000= F x 41m/s

i got F=2609.7560

Then for the incline plane the Watts should be the same but I am not sure what to do with the angle of the incline. Should I tack it on to the force? sin θ = 1/20 I guess that means the hypotenuse is 20 and the height of the incline is 1. And I am not sure where the weight of the car comes into play.

 

[rl.bhat]

Hi ddn87, welcome to PF.
Resolve the weight of the into two components. One perpendicular to inclined plane an other along the plane. This component opposes the motion of the car. Then find the net force. Using W = F*v , find the maximum velocity.

 

[ddn87]

Okay so

To find the angle we must find the arcsin(1/20) and i got the angle to be 2.86598 degrees

the weight is 1920 so the y component of this is 1920cos(2.86598)= 1917.5985
in the x direction is 1920sin(2.86598)=95.99987

So i would take 2609.7560-95.99987 =2513.756133 and plug it in as F in P=F x V?

 

[ddn87]

buti guess that means the speed increases which would not make sense if i subtract the x component from the original Net force.

 

[ddn87]

Thankyou rl.bhat!
I got the right answer, thanks for welcoming me! ill probably need lots of help through out this semester