Physics help, please?

Question

A van accelerates down a hill, going from rest to 30.0 m/s in 7.10 s. During the acceleration, a toy (m = 0.350 kg) hangs by a string from the van's ceiling. The acceleration is such that the string remains perpendicular to the ceiling.

Determine the angle of incline of the hill that the car is going down, and the tension of the string.

Thanks much!

Answer 1

Assuming constant acceleration

a=dv/dt= 30.0/7.10= 4.23m/s^2

To move the toy perpendicular to the van's ceiling

f=ma and f=mg sin(A)
where
mg is the weight of the toy
and mgsin(A) is the parallel to the ceiling component of weight as the string makes an angle A with the vertical.

So

sin(A) = ma/mg
A=arcSin(a/g)
A= arcSin(4.23/9.81)=25.5 degrees