# Finding the applied force at an angle?

Bethany

## Homework Statement

A 2000 kg car is driving up a 20° grade at a speed of 85 km/h. What force must be applied to the car to accelerate it up to 100 km/h in 10s?

m= 2000 kg
θ= 20°
Vo= 85 km/hr = 23.6 m/s
Vf = 100 km/hr = 27.8 m/s
t = 10 s

## Homework Equations

F = ma (Fx = max)
Fx= Fcosθ
Vox = Vo cosθ
Voy = Vo sinθ
Vx = Vox + axt
Vx= Vox +axt

## The Attempt at a Solution

I found these using the cos or sin equations above:
Vox = 22.1 m/s
Voy = 8.07 m/s
Vx = 26.1 m/s
Vy = 9.51 m/s

Using the last equation, I found ax = 0.4 m/s2

Fx= 800 N

I then solved for F using the second equation by dividing Fx by cosθ, making F= 851 N. I think I did something wrong when I solved for a, and my guess is that I couldn't use 10s for that since it was the incline, when I used it for the x values. I'm stuck on how to fix it, or on how to solve the problem a different way. These are practice problems that I have the answers to, but no solutions, so I know that F=7.5 kN.

I tried working backward and got that a=3.75 m/s2 and ax=3.52 m/s2. Using F=ma and the cos, I got Fx = 7040 N, which gets me the right answer however I do it. This makes me fairly certain that I'm doing something wrong with getting the acceleration.

Homework Helper
Gold Member

## Homework Statement

A 2000 kg car is driving up a 20° grade at a speed of 85 km/h. What force must be applied to the car to accelerate it up to 100 km/h in 10s?

m= 2000 kg
θ= 20°
Vo= 85 km/hr = 23.6 m/s
Vf = 100 km/hr = 27.8 m/s
t = 10 s

## Homework Equations

F = ma (Fx = max)
Fx= Fcosθ
Vox = Vo cosθ
Voy = Vo sinθ
Vx = Vox + axt
Vx= Vox +axt

## The Attempt at a Solution

I found these using the cos or sin equations above:
Vox = 22.1 m/s
Voy = 8.07 m/s
Vx = 26.1 m/s
Vy = 9.51 m/s

Using the last equation, I found ax = 0.4 m/s2

Fx= 800 N

I then solved for F using the second equation by dividing Fx by cosθ, making F= 851 N. I think I did something wrong when I solved for a, and my guess is that I couldn't use 10s for that since it was the incline, when I used it for the x values. I'm stuck on how to fix it, or on how to solve the problem a different way. These are practice problems that I have the answers to, but no solutions, so I know that F=7.5 kN.

I tried working backward and got that a=3.75 m/s2 and ax=3.52 m/s2. Using F=ma and the cos, I got Fx = 7040 N, which gets me the right answer however I do it. This makes me fairly certain that I'm doing something wrong with getting the acceleration.