Question

An engineer designs a roller coaster so that a car travels horizontally for 152 ft, then climbs 117 ft at an angle of 32.0° above the horizontal. It then moves 117 ft at an angle of 47.0° below the horizontal. If we take the initial horizontal motion of the car to be along the x-axis, what is the car's displacement?

Answer 1

`Total-displacement=T_d=331.0154354ft`

Step-by-step explanation:

Look at the picture I attached you. It's easy to see that you only need to use cosine identity in order to find the displacement along the x-axis:

`cos(\alpha )=(adjacent)/(hypotenuse)`

`d_1=displacement-1=152ft`

`d_2=displacement-2=d2_x=d2*cos(\alpha )=117*cos(32)=99.22162725ft`

`d_3=displacement-3=d3_x=d3*cos(\beta )=117*cos(47)=79.79380813ft`

Finally:

`T_d=d_1+d_2+d_3=152+99.22162725+79.79380813=331.0154354ft`