A pendulum bob is released from an initial height such that the speed of the bob at the bottom of the swing is 1.9 m/s. What is the initial height?

Question

Would this not be impossible to solve since there is no angle given at which the bob was released? From the book this was taken from the answer is supposedly 0.18m. The acceleration when the bob is $0^\circ$ to the horizontal is $9.81\cos 45^\circ$ (I think) and that does not match up with the displacement so honestly I have no ideas peft on how to solve this problem.

Answer 1

Using conservation of energy,

$$mgh=\frac12mv^2\implies h=\frac{v^2}{2g}$$

So $h=0.18399...$ (using $g=9.81$)